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.
Description
Identical-quantal binomial release models relate response mean and variance to release probability and an effective number of sites.
Identical-quantal binomial release models relate response mean and variance to release probability and an effective number of sites. Noise variance must be removed first.
The tool returns inferredReleaseProbability (inferred release probability); effectiveReleaseSiteCount (effective release site count). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Active Zone Number
Use Active Zone Number when you already have meanResponse, responseVariance, quantalMagnitude, measurementNoiseVariance and want inferredReleaseProbability, effectiveReleaseSiteCount. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Active Zone Number and understand its results
- Enter meanResponse, responseVariance, quantalMagnitude, 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 inferredReleaseProbability, effectiveReleaseSiteCount. 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 |
|---|---|---|---|
| meanResponse | Mean response | number | Required |
| responseVariance | Response variance | number | Required |
| quantalMagnitude | Quantal magnitude | number | Required |
| measurementNoiseVariance | Measurement noise variance | number | Required |
Require positive mean and quantum, nonnegative variances and corrected variance. Reject inferred probabilities outside (0,1].
p = 1−(responseVariance−noiseVariance)/(quantalMagnitude×meanResponse); N = meanResponse/(quantalMagnitude×p) The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"meanResponse": 10,
"responseVariance": 5,
"quantalMagnitude": 1,
"measurementNoiseVariance": 0
},
"output": {
"inferredReleaseProbability": 0.5,
"effectiveReleaseSiteCount": 20
}
}Limitations and assumptions
The effective site count can be noninteger. Independent identical sites and quanta are assumptions, not conclusions about physical active zones.
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. 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.
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.
- 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.