Calculator
Formula used
For a single exponential synaptic drive, the membrane response is modeled as:
Conductance-based inputs use a small-signal current amplitude:
Dendritic attenuation can be entered directly or approximated by exp(−x/λ).
How to use this calculator
- Choose a synapse model: conductance-based or current-based.
- Enter membrane parameters: input resistance and τm.
- Set synaptic decay τsyn and the number of synchronous synapses.
- Add attenuation using distance/λ or a direct factor.
- Optionally set a train length and frequency for summation.
- Press Calculate to view results above the form.
Example data
| Case | g peak (nS) | E syn (mV) | V rest (mV) | Rin (MΩ) | τm (ms) | τsyn (ms) | Atten | Peak (mV) |
|---|---|---|---|---|---|---|---|---|
| Distal small EPSP | 1.0 | 0 | -65 | 120 | 20 | 5 | 0.61 | ~4.1 |
| Proximal stronger EPSP | 2.5 | 0 | -70 | 80 | 15 | 3 | 0.85 | ~8.6 |
| Summating train | 1.2 | 0 | -65 | 120 | 20 | 5 | 0.60 | Higher with multiple events |
Article
1) What EPSP amplitude represents
An excitatory postsynaptic potential is a short depolarization caused by excitatory synaptic channels. This calculator reports the peak somatic voltage change in mV. Unitary somatic EPSPs are commonly ~0.1–1.0 mV, while coordinated inputs can reach several millivolts.
2) Conductance-based versus current-based inputs
Current-based inputs apply a peak current I0 (pA). Conductance-based inputs apply gpeak (nS) and depend on the driving force (Esyn − V). For fast estimates near rest, the tool uses I0 ≈ gpeak(Esyn − Vrest).
3) Input resistance sets the voltage scale
For small responses, ΔV scales with Rin because ΔV ≈ I·Rin. Many neurons span ~30–300 MΩ depending on type and state. If Rin doubles while synaptic drive stays constant, the predicted peak voltage roughly doubles.
4) τm and τsyn shape timing and width
τsyn sets how long synaptic drive persists, while τm sets membrane integration and decay. Typical τsyn for fast excitation is ~1–10 ms; τm is often ~10–30 ms. Faster τsyn usually yields earlier peaks and shorter rise times.
5) Peak time and rise time metrics
The peak time has a closed-form expression involving ln(τm/τsyn) for the exponential model. The calculator also estimates 10–90% rise time numerically from the generated trace, helping you compare synaptic kinetics across conditions without digitizing data.
6) Dendritic attenuation and distance
Somatic EPSPs can be much smaller than local dendritic events due to cable filtering. A practical first approximation is A = exp(−x/λ). For x=200 µm and λ=300 µm, A≈0.51, about half the local peak. When λ is unknown, enter a measured attenuation factor.
7) Temporal summation in event trains
When inputs repeat before full decay, voltages stack. The train option uses an exponential overlap approximation based on τm and the inter-event interval T=1000/f. Higher frequency or larger τm increases summation, raising the predicted train peak above single-event amplitude.
8) Interpreting outputs and limitations
This is a linear, passive estimate intended for small-to-moderate responses. It does not include voltage-gated currents, nonlinear driving-force changes at large depolarizations, or detailed morphology. Use it to sanity-check peaks, timing, and integrated area, and switch to compartmental models for strong or clustered inputs. When validating, compare predicted t_peak and rise time against traces, and adjust τsyn and attenuation before changing conductance or resistance parameters.
FAQs
1) What units does the calculator use?
Voltages are in mV, conductance in nS, current in pA, time constants in ms, distance and space constant in µm, and input resistance in MΩ. Results are reported in mV, ms, and mV·ms.
2) Why is my EPSP smaller when Vrest is less negative?
With conductance inputs, the driving force is (Esyn − Vrest). If Vrest moves closer to Esyn, the same gpeak produces less peak current, so the voltage response decreases.
3) What is a reasonable τsyn value for AMPA-like synapses?
Fast excitatory synapses often have decay time constants around 1–5 ms. Slower components or different receptor types can extend τsyn to 10–20 ms. Use values consistent with your preparation and temperature.
4) How should I choose attenuation if I do not know λ?
If you lack a morphology-based estimate, enter a direct attenuation factor between 0 and 1. You can calibrate it by matching a known somatic EPSP amplitude for a single synaptic event under similar conditions.
5) Does this include active dendritic conductances?
No. The model is linear and passive, intended for small-signal estimation. Active channels, NMDA voltage dependence, and dendritic spikes can substantially amplify or reshape EPSPs, especially during strong or clustered input.
6) Why does frequency affect the train peak?
Higher frequency shortens the interval between events, leaving less time for the membrane to decay. The remaining depolarization from previous events adds to the next, increasing the peak through temporal summation.
7) What does the area under EPSP indicate?
The mV·ms area approximates the time-integrated depolarization, which relates to delivered charge filtered by the membrane. It helps compare fast and slow synapses: two EPSPs can share similar peak amplitude yet differ greatly in total effect.