Fig. 1
From: Generalized leaky integrate-and-fire models classify multiple neuron types
Five generalized leaky integrate-and-fire (GLIF) models consisting of different phenomenological mechanisms are fit to electrophysiological data. A schematic describing the mechanisms is shown in a. Example data and models from two neurons of different transgenic lines are shown in b. For all models the input is a current, \(I_e(t)\), injected via a patch electrode illustrated in black at the top of b. Below the current are the voltage traces from four repeats of the same stimulus (here colors represent the different responses to the repeated stimuli and do not adhere to the standard color scheme in the rest of the manuscript). Below the biological data, the GLIF models are plotted. The output of the models is the trans-membrane potential, \(V(t)\), pictured in blue. When \(V(t)\) reaches a threshold, \(\Theta = \Theta _\infty + \Theta _S(t) + \Theta _v(t)\), shown in dashed green, a spike is produced, illustrated by blue dots. Note that the shape of the spike is not plotted as it is not fit by these models. Instead, after a refractory period, \(V(t)\) is reset to a value dependent on the specific model. The GLIF1 model is equivalent to the traditional LIF model with a refractory period where the model can not spike. This model contains one variable, \(V(t)\), and the threshold is fixed to a value we refer to as Θ∞. GLIF2 models include a second variable: a spike-induced threshold \(\Theta _S(t)\) which is added to the baseline threshold Θ∞. When the model spikes, \(\Theta _S(t)\), jumps up and then decays. Thus, after a spike, initially the total threshold is higher making it harder for the model to reach threshold. GLIF3 includes \(V(t)\) and two variables corresponding to two spike initiated after spike currents, \(I_j(t)\), which have different time constants and decay back to zero. The sum of the after-spike currents are illustrated in red. GLIF4 combines GLIF2 and GLIF3 for a total of four variables. GLIF5 includes an additional threshold component \(\Theta _v(t)\). \(\Theta _V(t)\) is dependent on the voltage of the model. Scale bars represent all model plots (not the amplitude of the current injection or biological voltage traces)
