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;
: Calcium ion accumulation with radial and longitudinal diffusion and pump

  SUFFIX cdp
  USEION ca READ cao, cai, ica WRITE cai, ica
  RANGE ica_pmp
  GLOBAL vrat, TotalBuffer, TotalPump
    : vrat must be GLOBAL--see INITIAL block
    : however TotalBuffer and TotalPump may be RANGE

DEFINE Nannuli 3

  (mol)   = (1)
  (molar) = (1/liter)
  (mM)    = (millimolar)
  (um)    = (micron)
  (mA)    = (milliamp)
  FARADAY = (faraday)  (10000 coulomb)
  PI      = (pi)       (1)

  DCa   = 0.8 (um2/ms)
  k1buf = 100 (/mM-ms) : Yamada et al. 1989
  k2buf = 0.1 (/ms)
  TotalBuffer = 0.003  (mM)

  k1    = 1       (/mM-ms)
  k2    = 0.005   (/ms)
  k3    = 1       (/ms)
  k4    = 0.005   (/mM-ms)
  : to eliminate pump, set TotalPump to 0 in hoc
  TotalPump = 1e-11  (mol/cm2)

  diam      (um)
  ica       (mA/cm2)
  ica_pmp   (mA/cm2)
  ica_pmp_last   (mA/cm2)
  parea     (um)     : pump area per unit length
  cai       (mM)
  cao       (mM)
  vrat[Nannuli]  (1) : dimensionless
                     : numeric value of vrat[i] equals the volume 
                     : of annulus i of a 1um diameter cylinder
                     : multiply by diam^2 to get volume per um length
  Kd        (/mM)
  B0        (mM)

CONSTANT { volo = 1e10 (um2) }

  : ca[0] is equivalent to cai
  : ca[] are very small, so specify absolute tolerance
  : let it be ~1.5 - 2 orders of magnitude smaller than baseline level
  ca[Nannuli]       (mM) <1e-7>
  CaBuffer[Nannuli] (mM) <1e-5>
  Buffer[Nannuli]   (mM) <1e-5>
  pump              (mol/cm2) <1e-15>
  pumpca            (mol/cm2) <1e-15>

  SOLVE state METHOD sparse
  ica_pmp_last = ica_pmp
  ica = ica_pmp

LOCAL factors_done

   if (factors_done == 0) {  : flag becomes 1 in the first segment
      factors_done = 1       :   all subsequent segments will have
      factors()              :   vrat = 0 unless vrat is GLOBAL

  Kd = k1buf/k2buf
  B0 = TotalBuffer/(1 + Kd*cai)

  FROM i=0 TO Nannuli-1 {
    ca[i] = cai
    Buffer[i] = B0
    CaBuffer[i] = TotalBuffer - B0

  parea = PI*diam

: Manually computed initalization of pump
: assumes that cai has been equal to cai0_ca_ion for a long time
:  pump = TotalPump/(1 + (cai*k1/k2))
:  pumpca = TotalPump - pump
: If possible, instead of using formulas to calculate pump and pumpca,
: let NEURON figure them out--just uncomment the following four statements
  ica_pmp = 0
  ica_pmp_last = 0
  SOLVE state STEADYSTATE sparse
: This requires that pump and pumpca be constrained by the CONSERVE
: statement in the STATE block.
: If there is a voltage-gated calcium current, 
: this is almost certainly the wrong initialization. 
: In such a case, first do an initialization run, then use SaveState
: On subsequent runs, restore the initial condition from the saved states.

LOCAL frat[Nannuli]  : scales the rate constants for model geometry
PROCEDURE factors() {
  LOCAL r, dr2
  r = 1/2                : starts at edge (half diam)
  dr2 = r/(Nannuli-1)/2  : full thickness of outermost annulus,
                         : half thickness of all other annuli
  vrat[0] = 0
  frat[0] = 2*r
  FROM i=0 TO Nannuli-2 {
    vrat[i] = vrat[i] + PI*(r-dr2/2)*2*dr2  : interior half
    r = r - dr2
    frat[i+1] = 2*PI*r/(2*dr2)  : outer radius of annulus
                                : div by distance between centers
    r = r - dr2
    vrat[i+1] = PI*(r+dr2/2)*2*dr2  : outer half of annulus

LOCAL dsq, dsqvol  : can't define local variable in KINETIC block
                   :   or use in COMPARTMENT statement

KINETIC state {
  COMPARTMENT i, diam*diam*vrat[i] {ca CaBuffer Buffer}
  COMPARTMENT (1e10)*parea {pump pumpca}
  COMPARTMENT volo {cao}
  LONGITUDINAL_DIFFUSION i, DCa*diam*diam*vrat[i] {ca}

  ~ ca[0] + pump <-> pumpca  (k1*parea*(1e10), k2*parea*(1e10))
  ~ pumpca <-> pump + cao    (k3*parea*(1e10), k4*parea*(1e10))
  CONSERVE pump + pumpca = TotalPump * parea * (1e10)
  ica_pmp = 2*FARADAY*(f_flux - b_flux)/parea

  : all currents except pump
  : ica is Ca efflux
  ~ ca[0] << (-(ica - ica_pmp_last)*PI*diam/(2*FARADAY))
  FROM i=0 TO Nannuli-2 {
    ~ ca[i] <-> ca[i+1]  (DCa*frat[i+1], DCa*frat[i+1])
  dsq = diam*diam
  FROM i=0 TO Nannuli-1 {
    dsqvol = dsq*vrat[i]
    ~ ca[i] + Buffer[i] <-> CaBuffer[i]  (k1buf*dsqvol, k2buf*dsqvol)
  cai = ca[0]

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