Quantal Release Statistics: 2D Synapse Model

Stimulation

True Parameters

Release sites N 40

Release probability p 0.30

Quantal amplitude q 0.50 mV

This Trial

Press "Fire One Trial" to release from N independent Bernoulli sites.

Quanta released (k)

–

EPP amplitude

–

Quantal Analysis (recovered from data)

Trials collected

Mean / Variance

– / –

p̂ estimate

–

N̂ estimate

–

How it works

Real neurotransmitter release is quantal: each of N docked vesicles fuses independently on a given trial with probability p (a Bernoulli trial per site), so the number of quanta k released on one trial is binomially distributed:

P(k) = C(N,k) · p^k · (1-p)^(N-k)
mean:     m = N·p
variance: σ² = N·p·(1-p)

Each released quantum adds one fixed increment q to the total end-plate-potential amplitude, so amplitude = k·q. Run enough trials and the histogram of amplitudes shows the tell-tale multi-peaked quantal structure — separate bumps at 0, q, 2q, 3q… — first described by del Castillo & Katz (1954).

Quantal analysis works the statistics backwards: from just the mean and variance of many trials' amplitudes, you can recover the two hidden parameters N and p without ever counting sites directly:

σ²/mean = (1-p)·q  →  p̂ = 1 − σ²/(mean·q)
N̂ = mean / (p̂·q)

Watch p̂ and N̂ converge onto the true sliders as trial count grows — exactly the "indirect" or coefficient-of-variation method physiologists use on real intracellular recordings, where N and p can never be observed directly.

Release site (armed) Released quantum Site (did not release)