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Fast Spiking Basket cells (Tzilivaki et al 2019)

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"Interneurons are critical for the proper functioning of neural circuits. While often morphologically complex, dendritic integration and its role in neuronal output have been ignored for decades, treating interneurons as linear point neurons. Exciting new findings suggest that interneuron dendrites support complex, nonlinear computations: sublinear integration of EPSPs in the cerebellum, coupled to supralinear calcium accumulations and supralinear voltage integration in the hippocampus. These findings challenge the point neuron dogma and call for a new theory of interneuron arithmetic. Using detailed, biophysically constrained models, we predict that dendrites of FS basket cells in both hippocampus and mPFC come in two flavors: supralinear, supporting local sodium spikes within large-volume branches and sublinear, in small-volume branches. Synaptic activation of varying sets of these dendrites leads to somatic firing variability that cannot be explained by the point neuron reduction. Instead, a 2-stage Artificial Neural Network (ANN), with both sub- and supralinear hidden nodes, captures most of the variance. We propose that FS basket cells have substantially expanded computational capabilities sub-served by their non-linear dendrites and act as a 2-layer ANN."
1 . Tzilivaki A, Kastellakis G, Poirazi P (2019) Challenging the point neuron dogma: FS basket cells as 2-stage nonlinear integrators Nature Communications 10(1):3664 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism: Hippocampus; Prefrontal cortex (PFC);
Cell Type(s): Hippocampus CA3 interneuron basket GABA cell; Neocortex layer 5 interneuron;
Gap Junctions:
Simulation Environment: NEURON; MATLAB; Python;
Model Concept(s): Active Dendrites; Detailed Neuronal Models;
Implementer(s): Tzilivaki, Alexandra [alexandra.tzilivaki at]; Kastellakis, George [gkastel at];
Search NeuronDB for information about:  Hippocampus CA3 interneuron basket GABA cell;
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TITLE simple AMPA receptors


	Simple model for glutamate AMPA receptors


    Whole-cell recorded postsynaptic currents mediated by AMPA/Kainate
    receptors (Xiang et al., J. Neurophysiol. 71: 2552-2556, 1994) were used
    to estimate the parameters of the present model; the fit was performed
    using a simplex algorithm (see Destexhe et al., J. Computational Neurosci.
    1: 195-230, 1994).


    The simplified model was obtained from a detailed synaptic model that 
    included the release of transmitter in adjacent terminals, its lateral 
    diffusion and uptake, and its binding on postsynaptic receptors (Destexhe
    and Sejnowski, 1995).  Short pulses of transmitter with first-order
    kinetics were found to be the best fast alternative to represent the more
    detailed models.


    The first-order model can be solved analytically, leading to a very fast
    mechanism for simulating synapses, since no differential equation must be
    solved (see references below).


   Destexhe, A., Mainen, Z.F. and Sejnowski, T.J.  An efficient method for
   computing synaptic conductances based on a kinetic model of receptor binding
   Neural Computation 6: 10-14, 1994.  

   Destexhe, A., Mainen, Z.F. and Sejnowski, T.J. Synthesis of models for
   excitable membranes, synaptic transmission and neuromodulation using a 
   common kinetic formalism, Journal of Computational Neuroscience 1: 
   195-230, 1994.


	RANGE R, gmax, g             
	NONSPECIFIC_CURRENT  iglu             : i
	GLOBAL Cdur, Alpha, Beta, Erev, Rinf, Rtau
	(nA) = (nanoamp)
	(mV) = (millivolt)
	(umho) = (micromho)
	(mM) = (milli/liter)

        Cmax	= 1	(mM)		: max transmitter concentration
	Cdur	= 0.3	(ms)		: transmitter duration (rising phase)
	Alpha	= 10	(/ms)		: forward (binding) rate
	Beta	= 0.11	(/ms)		: backward (unbinding) rate
        Erev	= 0	(mV)		:0 reversal potential

	v		(mV)		: postsynaptic voltage
	iglu 		(nA)		: current = g*(v - Erev)     :i
	g 		(umho)		: conductance
	Rinf				: steady state channels open
	Rtau		(ms)		: time constant of channel binding

STATE {Ron Roff}

        Rinf = Cmax*Alpha / (Cmax*Alpha + Beta)
       	Rtau = 1 / ((Alpha * Cmax) + Beta)
	synon = 0

	SOLVE release METHOD cnexp
	g = (Ron + Roff)*1(umho)
	iglu = g*(v - Erev)  :i

DERIVATIVE release {
	Ron' = (synon*Rinf - Ron)/Rtau
	Roff' = -Beta*Roff

: following supports both saturation from single input and
: summation from multiple inputs
: if spike occurs during CDur then new off time is t + CDur
: ie. transmitter concatenates but does not summate
: Note: automatic initialization of all reference args to 0 except first

NET_RECEIVE(weight, on, nspike, r0, t0 (ms)) {
	: flag is an implicit argument of NET_RECEIVE and  normally 0
        if (flag == 0) { : a spike, so turn on if not already in a Cdur pulse
		nspike = nspike + 1
		if (!on) {
			r0 = r0*exp(-Beta*(t - t0))
			t0 = t
			on = 1
			synon = synon + weight
			state_discontinuity(Ron, Ron + r0)
			state_discontinuity(Roff, Roff - r0)
		: come again in Cdur with flag = current value of nspike
		net_send(Cdur, nspike)
	if (flag == nspike) { : if this associated with last spike then turn off
		r0 = weight*Rinf + (r0 - weight*Rinf)*exp(-(t - t0)/Rtau)
		t0 = t
		synon = synon - weight
		state_discontinuity(Ron, Ron - r0)
		state_discontinuity(Roff, Roff + r0)
		on = 0

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