LGMD impedance (Dewell & Gabbiani 2019)

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"How neurons filter and integrate their complex patterns of synaptic inputs is central to their role in neural information processing . Synaptic filtering and integration are shaped by the frequency-dependent neuronal membrane impedance. Using single and dual dendritic recordings in vivo, pharmacology, and computational modeling, we characterized the membrane impedance of a collision detection neuron in the grasshopper, Schistocerca americana. This neuron, the lobula giant movement detector (LGMD), exhibits consistent impedance properties across frequencies and membrane potentials. Two common active conductances gH and gM, mediated respectively by hyperpolarization-activated cyclic nucleotide gated (HCN) channels and by muscarine sensitive M-type K+ channels, promote broadband integration with high temporal precision over the LGMD's natural range of membrane potentials and synaptic input frequencies. Additionally, we found that a model based on the LGMD's branching morphology increased the gain and decreased the delay associated with the mapping of synaptic input currents to membrane potential. More generally, this was true for a wide range of model neuron morphologies, including those of neocortical pyramidal neurons and cerebellar Purkinje cells. These findings show the unexpected role played by two widespread active conductances and by dendritic morphology in shaping synaptic integration."
1 . Dewell RB, Gabbiani F (2019) Active membrane conductances and morphology of a collision detection neuron broaden its impedance profile and improve discrimination of input synchrony. J Neurophysiol [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell; Dendrite;
Brain Region(s)/Organism:
Cell Type(s): Locust Lobula Giant Movement Detector (LGMD) neuron;
Channel(s): I h; I M;
Gap Junctions:
Simulation Environment: NEURON;
Model Concept(s): Active Dendrites; Detailed Neuronal Models; Synaptic Integration; Membrane Properties;
Implementer(s): Dewell, Richard Burkett [dewell at bcm.edu];
Search NeuronDB for information about:  I M; I h;
TITLE K-D channel with alpha and beta rates from RBD

        (mA) = (milliamp)
        (mV) = (millivolt)
        (S) = (siemens)
        (mS) = (millisiemens)

    : note - every variable accessible in NEURON will be having the suffix _KD2

        SUFFIX KD2
        USEION k READ ek WRITE ik
        RANGE gmax, g

: all values can be adjusted in hoc files
    gmax= 0.001 (S/cm2)
    np = 3		(1)

	kan=10.5	(mV)	:sets steepness of alpha
	Aan=3.0		(/ms)
	dan=-17		(mV)	:sets inflection point of beta
	kbn=30		(mV)	:sets steepness of beta
	Abn=0.12	(/ms)
	dbn=-50		(mV)
	kal=35		(mV)	:sets steepness of alpha
	Aal=0.00025	(/ms) :1/Aah changes tau at hyperpolarized potentials
	dal=-85		(mV)	:sets inflection point of alpha
	kbl=4.8		(mV)	:sets steepness of beta
	Abl=0.0033	(/ms) :1/Abh sets tau at depolarized potentials 
	dbl=-51		(mV)	:sets inflection point of beta

    v (mV)
    ek (mV)
    ik (mA/cm2)
    an (/ms)
    bn (/ms)
    al (/ms)
    bl (/ms)
	g (S/cm2)


    SOLVE states METHOD cnexp
    g  = gmax*n^np*l
    ik  = g*(v-ek)

    n = an/(an+bn)
    l = al/(al+bl)

DERIVATIVE states {  
    n' = ((an*(1-n)) - (bn*n))
    l' = ((al*(1-l)) - (bl*l))

PROCEDURE settables(v (mV)) {
    TABLE an, bn, al, bl DEPEND dan, dbn, dal, dbl, Aan, Abn, Aal, Abl
          FROM -100 TO 50 WITH 750

    if (v == dan) {
    	an = Aan
	} else {
		an = -Aan/kan*(dan-v) / (1 - exp((dan-v)/kan))	: forward rate of activation (/ms)
	bn = Abn*exp( (dbn-v)/kbn)	: backward activation rate (/ms)
	al = Aal*exp( (dal-v)/kal)	: forward inactivation rate (/ms)
	bl = Abl/(exp( (dbl-v)/ kbl) + 1)	: backward inactivation rate (/ms)

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