Modeling Neural Activity

Table 1

Overview of the dimensionality of cellular models.

		Amplifying	Resonant
	Membrane potential; (𝑉)	Inward current activation	Inward current inactivation	Outward current activation	Leak current capacitance; (not time dependent)	Physiological AP mechanism
Hodgkin and Huxley [1]	1	(𝑚) 2	(ℎ) 3	(𝑛) 4	Yes	Yes
FitzHugh-Nagumo [9, 10]	1	Instantaneous; (not time dependent)	Generic recovery	(𝑤) 2	Yes	Yes
Morris and Lecar [12]; (Ca instead of Na)	1	Instantaneous; (not time dependent)	No	(𝑤) 2	Yes	Yes
IF [13]	1	No	No	No	Yes	Generator
RF [15]	1	No	No	Simplified (𝐿) 2	Yes	Generator
QIF [14]	1	Generic amplification; (quadratic)	No	No	Yes	Reset
Izhikevich SMC [15]	1	Generic amplification; (quadratic)	No	Simplified (𝐿) 2	Yes	Reset

AP: action potential; L: inductor; IF: integrate and fire; QIF: quadratic integrate and fire; RF: resonate and Fire; SMC: simple model of choice; V, m, h, n: parameters of the Hodgkin and Huxley equations; w: recovery variable. Numbers 1–4 count the dimensions of the model.