Description
Calculate a two-point MSD slope and a conditional diffusion-model term.
Biophysical scalar models require explicit signal, concentration, temperature, energy and geometric conventions. Effective concentration differs from dimensionless activity, a single displacement differs from mean-square displacement, and a fluorescence yield ratio needs absorption and refractive-index corrections. Supplied model parameters do not establish that the model applies to an experiment.
Calculate a two-point MSD slope and a conditional diffusion-model term.
When to use this tool
Use Diffusion MSD Local Slope when you already have firstTime, secondTime, firstMsd, secondMsd, dimensions and need to calculate a two-point MSD slope and a conditional diffusion-model term.
How to use the tool and how it works
- Enter firstTime, secondTime, firstMsd, secondMsd, dimensions. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read msdSlope, diffusionEstimate. Use the output convention below.
Require secondTime>firstTime, nonnegative MSD values and whole dimensions 1..3; slope=(secondMSD-firstMSD)/(secondTime-firstTime), estimate=slope/(2*dimensions).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstTime | First Time | Required. Finite number. |
| secondTime | Second Time | Required. Finite number. |
| firstMsd | First Msd | Required. Finite number; minimum 0. |
| secondMsd | Second Msd | Required. Finite number; minimum 0. |
| dimensions | Dimensions | Required. Safe integer; minimum 1; maximum 3. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| msdSlope | Msd Slope | Required. Finite number. |
| diffusionEstimate | (secondMsd-firstMsd)/(secondTime-firstTime)/(2*dimensions); a local normal-isotropic-diffusion interpretation, retaining negative slopes. | Required. Finite number. |
{
"input": {
"firstTime": 1,
"secondTime": 3,
"firstMsd": 4,
"secondMsd": 12,
"dimensions": 2
},
"output": {
"msdSlope": 4,
"diffusionEstimate": 1
}
}Limitations and assumptions
- Negative slopes and diffusion estimates are retained. This assumes a linear isotropic normal-diffusion MSD relation; no trajectory, ensemble average, valid regime, fit or physical diffusion coefficient is established.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the complete physical model, calibrated measurements and uncertainty analysis. Check reference states, photon-signal bases, diffusion assumptions and binding-constant conventions before interpreting local contributions as physical measurements.
References
Similar or alternative tools
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