The F–I Curve & Strengths/Weaknesses
We just saw more input → faster firing. Plot that relationship — firing rate vs input current — and you get the F–I curve (frequency–current curve). It's one of the most important summaries of a neuron's behavior.
Slide the current and trace out the curve. For each input I, we run the spiking simulation and count spikes per second (Hz):
Below the "rheobase" current (~2.5 nA) the neuron is silent — 0 Hz. Past it, firing rate climbs with input. This F–I curve is exactly the transfer function you met in the last tutorial — except now we derived it from a real neuron model instead of just assuming an S-shape. Its slope is the neuron's gain.
🎯 The big reveal: this F–I curve IS the transfer function from the previous tutorial — the S-shaped 'input → firing rate' curve. Back then we just assumed that S-shape. Now you've derived it from an actual neuron model (the LIF). And its slope is the neuron's gain. Two tutorials, one idea, finally connected.
Why the LIF model is a great starting point — strengths:
• It has an exact solution (rare and lovely).
• It's easy to interpret (leaky bucket).
• It's a fantastic building block for networks of thousands of neurons.
And where it falls short — weaknesses:
• The spike is an artificial discontinuity (bolted on, not emergent).
• It's an abstraction — a real neuron is far messier.
• It can only produce one firing pattern (steady spiking) — real neurons burst, adapt, and do much more.
Those limits are exactly why richer models (Hodgkin–Huxley, Izhikevich) exist.