Input Parameters
Calculation Results Table
Use the buttons below to export the current results table as CSV or PDF.
| Temperature (°C | Solvent viscosity (cP) | Hydrodynamic radius (nm) | Absolute temperature (K) | Viscosity (Pa·s) | Radius (m) | D (m²/s) | D (µm²/s) |
|---|---|---|---|---|---|---|---|
| Run a calculation to populate this table. | |||||||
Example Data Table
This illustrative table shows approximate diffusion coefficients for several proteins at 25 °C in water.
| Protein | Hydrodynamic radius (nm) | Temperature (°C) | Viscosity (cP) | Estimated D (µm²/s) |
|---|---|---|---|---|
| Lysozyme | 1.9 | 25 | 0.89 | 110 |
| BSA (monomer) | 3.5 | 25 | 0.89 | 60 |
| IgG | 5.5 | 25 | 0.89 | 40 |
| Small peptide | 0.8 | 25 | 0.89 | 260 |
Formula Used
The calculator is based on the Stokes–Einstein equation for translational diffusion:
D = kB T / (6 π η r)
- D is the diffusion coefficient (m²/s).
- kB is Boltzmann’s constant (1.380649 × 10−23 J/K).
- T is absolute temperature (K).
- η is solvent viscosity (Pa·s).
- r is the hydrodynamic radius of the protein (m).
Viscosity in centipoise is converted to pascal seconds, and hydrodynamic radius in nanometers is converted to meters before evaluating the expression.
How to Use This Calculator
- Enter the experimental temperature and select whether it is reported in degrees Celsius or Kelvin.
- Specify the solvent viscosity in centipoise, using buffer specific values when available.
- Provide an estimated hydrodynamic radius for the protein or peptide in nanometers.
- Click Calculate diffusion coefficient to compute D in m²/s and µm²/s.
- Review the results table, then export values as CSV or PDF for further analysis or record keeping.
All results are approximate and intended for educational and planning purposes only.
Protein Diffusion Coefficient Article
1. Understanding protein diffusion coefficients
Protein diffusion coefficients describe how fast protein molecules move through solution under Brownian motion. They link microscopic motion to macroscopic observables like band broadening, reaction rates, and transport in cells or materials. Accurately estimating diffusion helps interpret chromatography, electrophoresis, and time‑resolved spectroscopy experiments, especially when direct measurements are noisy or unavailable. They provide a critical bridge between molecular structure, solvent environment, and observed experimental behavior across many biophysical techniques.
2. Factors influencing diffusion behavior
Diffusion depends strongly on temperature, solvent viscosity, and hydrodynamic radius. Higher temperature generally increases molecular mobility, while more viscous solvents slow motion dramatically. Protein shape, aggregation state, and bound ligands effectively change the hydrodynamic radius, altering friction with the solvent and therefore the observed diffusion coefficient values across different experimental conditions. Even small temperature differences or modest viscosity changes can shift diffusion enough to influence assay timing and interpretation.
3. Using the Stokes–Einstein relationship
This calculator implements the widely used Stokes–Einstein equation for spherical particles. It relates diffusion to Boltzmann’s constant, absolute temperature, solvent viscosity, and particle radius in a simple algebraic expression. Although proteins are rarely perfect spheres, the approximation is extremely useful for first‑pass design, feasibility checks, sanity‑checking diffusion measurements, and teaching core transport concepts.
4. Choosing meaningful input parameters
For reliable predictions, match units carefully and use experimentally justified values. Temperature should reflect the actual sample environment, not room temperature defaults from catalog entries. Viscosity values should be chosen for the specific buffer composition, not pure water, especially when glycerol, sugars, crowding agents, or organic cosolvents significantly thicken the solution and slow molecular motion.
5. Interpreting numerical diffusion outputs
The calculator reports diffusion in square meters per second and micrometers squared per second. Large globular proteins show smaller coefficients than compact peptides or fragments. Comparing calculated values across conditions helps highlight how temperature shifts or formulation changes influence mobility, residence times, and mixing within microfluidic channels, chromatographic columns, or crowded cellular environments.
6. Connecting with related biophysical tools
Diffusion analysis complements charge state and spectroscopic calculations. For example, the Amino Acid Charge vs pH Calculator helps you understand how protonation affects protein interactions and aggregation. Likewise, the Peptide Molar Extinction Calculator links concentration and absorbance for kinetic, binding, or transport studies.
7. Practical tips for experimental planning
By exploring different temperatures, viscosities, and radii, you can map diffusion regimes relevant to your experiments. Combine calculated coefficients with empirical measurements for robust modeling and parameter fitting. Over time, this integrated approach improves buffer selection, instrument settings, and assay robustness. Thoughtful planning today saves many frustrating troubleshooting cycles later. Saving representative parameter sets also creates a reusable knowledge base for future projects.
Frequently Asked Questions
Why do I need the hydrodynamic radius, not just molecular weight?
Molecular weight does not uniquely determine how a protein occupies space in solution. Hydrodynamic radius captures shape, solvation, and compactness, which directly control friction and diffusion behavior.
Can I use this calculator for membrane proteins or complexes?
You can, but results will be approximate because membrane proteins, fibrils, and large complexes deviate strongly from spherical geometry. Treat the output as a guideline, and rely on experimental measurements when possible.
How accurate are diffusion coefficients projected from the Stokes–Einstein equation?
For roughly spherical, monomeric proteins in dilute solution, predictions are typically within tens of percent. Deviations increase with crowding, anisotropic shapes, strong interactions, or uncertain radius values, so always consider experimental validation.
Which viscosity value should I use for buffered samples?
Use viscosity measured or tabulated for the exact buffer composition, including salts, glycerol, sugars, or cosolvents. Assuming pure water viscosity often underestimates friction, giving diffusion coefficients that are unrealistically high for real formulations.
Can I compare results from this tool with chromatography data?
Yes. Diffusion coefficients help interpret band broadening, peak widths, and plate counts in size‑exclusion or field‑flow fractionation methods. Ensure that you use matching temperatures, buffer viscosities, and protein states when making quantitative comparisons.
Is it possible to invert the calculation to estimate radius?
In principle, you can algebraically rearrange the Stokes–Einstein equation to solve for radius given an experimental diffusion coefficient. This page focuses on forward calculations, but the relationship remains symmetric and can be inverted manually.