Quantal Size
Estimate quantal amplitude as noise-corrected variance/mean under identical-quantal Poisson release; finite-p binomial release and quantal variability violate this approximation.
Description
A Poisson quantal model links response variance to mean through quantal size.
A Poisson quantal model links response variance to mean through quantal size. Subtracting measurement-noise variance isolates the modelled response variability.
The tool returns meanResponse (mean response); noiseCorrectedVariance (noise corrected variance); estimatedQuantalSize (estimated quantal size). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Quantal Size
Use Quantal Size when you already have responseMagnitudes, measurementNoiseVariance and want meanResponse, noiseCorrectedVariance, estimatedQuantalSize. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Quantal Size and understand its results
- Enter responseMagnitudes, measurementNoiseVariance using the field table below. Match the units, ordering and data boundaries described in the calculation.
- Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
- Read meanResponse, noiseCorrectedVariance, estimatedQuantalSize. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
- Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| responseMagnitudes | Response magnitudes | list of number | Required |
| measurementNoiseVariance | Measurement noise variance | number | Required |
Require nonnegative responses, positive mean and strictly positive corrected sample variance. At least two responses are needed.
q estimate = (sampleVariance(response)−noiseVariance)/mean(response) The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"responseMagnitudes": [
1,
3,
5
],
"measurementNoiseVariance": 1
},
"output": {
"meanResponse": 3,
"noiseCorrectedVariance": 3,
"estimatedQuantalSize": 1
}
}Limitations and assumptions
The result assumes Poisson release and identical quanta. Incorrect noise variance or other variability sources can invalidate the estimate.
Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.
Alternative or Complementary methods
Release Probability: Invert observed failure fraction F=(1−p)^N using supplied identical independent release sites; the boundary estimate p=1 does not imply certainty about underlying p. Active Zone Number: Infer effective release-site count and p from binomial mean/variance and independently measured quantal magnitude; N is not rounded or claimed to count anatomical active zones.
Methodological background: Quantal components of the end-plate potential.1
References
-
Quantal components of the end-plate potential — del Castillo and Katz; Journal of Physiology
Similar or alternative tools
- Release Probability
Invert observed failure fraction F=(1−p)^N using supplied identical independent release sites; the boundary estimate p=1 does not imply certainty about underlying p.
- Active Zone Number
Infer effective release-site count and p from binomial mean/variance and independently measured quantal magnitude; N is not rounded or claimed to count anatomical active zones.