Heterogeneous Quantal Release Simulation

Different release sites

Choose n = 1, 2, or 3 release sites. Each site i has its own release probability p_i and quantal amplitude q_i (pA). A site releases either zero or one quantum, independently of the other sites; released amplitudes add linearly. The model calculates every release/failure combination and combines probabilities when different combinations give the same amplitude.

With three sites, there can be up to eight distinct amplitudes, including zero. Without measurement noise, mean = Σp_iq_i, variance = Σp_i(1 − p_i)q_i², and the failure probability is the product of all (1 − p_i).

Connect to the binomial model

Select Use the same release probability to make active sites use p₁, and Use the same quantal amplitude to make them use q₁. With both selected, this reduces to the binomial model. Clear either checkbox to explore departures from its identical-site assumptions. Independence is still assumed: this simulation does not model correlated release.

Different p values change the probabilities of release combinations. Different q values change their amplitudes and can produce irregular peak spacing. If q differs but p is identical, the number of releases is still binomial, but EPSC amplitude is no longer a single fixed q times that number.

Read the plots

The upper plot shows the theoretical distribution of EPSC amplitudes, displayed as positive magnitudes in pA. These are calculated probabilities, not a finite set of randomly generated trials. With Noise = 0, the point at zero represents release failures. The cumulative plot gives the predicted percentage of responses at or below each amplitude.

Show as histogram groups probability into amplitude bins. With noise, the ordinary curve shows probability assigned to small numerical intervals; histogram bars combine these intervals. Their heights therefore depend on bin width: do not compare curve heights directly with histogram heights. White markers indicate the underlying noiseless response amplitudes.

Noise and summary statistics

Noise is the standard deviation of additive, zero-mean Gaussian measurement noise, in pA. It broadens each response peak, can obscure failures, and can produce apparent negative amplitudes around zero. It does not change the release probabilities.

Show more displays the theoretical mean, standard deviation (sDev), and coefficient of variation (CV = SD / mean). These statistics describe release variability only; they exclude the added measurement noise. For independent measurement noise, the measured variance would be the release variance plus Noise squared. CV is undefined when the mean is zero. Total p is the numerically summed probability, normally close to 1; finite plotting limits and numerical approximation can cause small deviations.

Controls and figures

Use the sliders or edit the number fields; plots update automatically. The max fields set control limits, not additional biological parameters. Text size adjusts graph and parameter text. Hover over controls for explanations and graphs for values; use a graph’s camera button to save a PNG. CSV data saves parameters, individual release combinations, merged amplitudes, and the displayed distribution. Reset restores the model parameters.

Try it

1. Set n = 3, Noise = 0, and select both same-value checkboxes. Set p₁ = 0.5 and q₁ = 6. Compare with the binomial simulation using the same settings.
2. Clear the probability checkbox and set p values to 0.1, 0.5, and 0.9. The mean remains the same as with three p values of 0.5, but the variance changes.
3. Keep probabilities equal, clear the amplitude checkbox, and set q values to 3, 6, and 12 pA. Identify which release combinations produce each peak.
4. Increase Noise. Can different underlying release-site arrangements produce distributions that are difficult to distinguish?

Each site’s q is fixed; the model does not include trial-to-trial quantal-size variation, multivesicular release at an individual site, or short-term plasticity. A smooth-looking amplitude distribution alone does not establish that release sites are identical.

References

Experimental evidence that release probability can differ among terminals and release sites is discussed by Murthy, Sejnowski & Stevens (1997), Heterogeneous Release Properties of Visualized Individual Hippocampal Synapses, and Rosenmund, Clements & Westbrook (1993), Nonuniform Probability of Glutamate Release at a Hippocampal Synapse.