Double cable myelinated axon (Layer 5 pyramidal neuron; Cohen et al 2020)

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The periaxonal space in myelinated axons is conductive (~50 ohm cm). Together with a rapidly charging myelin sheath and relatively sealed paranodes, periaxonal conduction shapes the saltating voltage profiles of transaxonal (Vm), transmyelin (Vmy) and transfibre (Vmym) potentials. This model exemplifies double cable saltatory conduction across both time and space, and is the same cell (#6) as seen in Movie S4 of Cohen et al. 2020. This model version allows one to visualize and manipulate the controlling parameters of a propagating action potential. Further notes: The corresponding potentials in NEURON to those named above are v, vext (or vext[0]) and v+vext, respectively. The loaded biophysical parameters were those optimized for this cell (Cohen et al. 2020).
1 . Cohen CCH, Popovic MA, Klooster J, Weil M, Möbius W, Nave K, Kole MHP (2020) Saltatory Conduction along Myelinated Axons Involves a Periaxonal Nanocircuit Cell
Model Information (Click on a link to find other models with that property)
Model Type: Axon; Channel/Receptor; Dendrite; Extracellular; Glia; Neuron or other electrically excitable cell;
Brain Region(s)/Organism:
Cell Type(s): Neocortex L5/6 pyramidal GLU cell; Myelinated neuron;
Channel(s): Ca pump; I Calcium; I h; I K,Ca; I K,leak; I L high threshold; I T low threshold; I M; I Na,p; I Na,t; I Sodium; I Potassium;
Gap Junctions:
Simulation Environment: NEURON;
Model Concept(s): Action Potentials; Active Dendrites; Axonal Action Potentials; Conductance distributions; Conductances estimation; Detailed Neuronal Models; Electrotonus; Extracellular Fields; Membrane Properties; Multiple sclerosis; Parameter sensitivity; Double cable;
Implementer(s): Cohen, Charles CH [c.cohen at]; Kole, Maarten [m.kole at];
Search NeuronDB for information about:  Neocortex L5/6 pyramidal GLU cell; I Na,p; I Na,t; I L high threshold; I T low threshold; I K,leak; I M; I h; I K,Ca; I Sodium; I Calcium; I Potassium; Ca pump;
: Eight state kinetic sodium channel gating scheme
: Modified from k3st.mod, chapter 9.9 (example 9.7)
: of the NEURON book
: 12 August 2008, Christoph Schmidt-Hieber
: accompanies the publication:
: Schmidt-Hieber C, Bischofberger J. (2010)
: Fast sodium channel gating supports localized and efficient 
: axonal action potential initiation.
: J Neurosci 30:10233-42
: Made threadsafe (CCohen)

    SUFFIX nax
    USEION na READ ena WRITE ina
    GLOBAL vShift, vShift_inact, maxrate
    RANGE vShift_inact_local
    RANGE gna, gbar, ina_inax
    RANGE a1_0, a1_1, b1_0, b1_1, a2_0, a2_1
    RANGE b2_0, b2_1, a3_0, a3_1, b3_0, b3_1
    RANGE bh_0, bh_1, bh_2, ah_0, ah_1, ah_2

UNITS { (mV) = (millivolt) }

: Initialize parameters


:   gbar = 33                       (millimho/cm2)
    gbar = 1000                     (pS/um2)

    a1_0 = 6.264774039489168e+01    (/ms)
    a1_1 = 1.160554780103536e-02    (/mV) 

    b1_0 = 1.936911472259165e-03    (/ms)
    b1_1 = 1.377185203515948e-01    (/mV)

    a2_0 = 3.478282276988217e+01    (/ms)
    a2_1 = 2.995594783341219e-02    (/mV) 

    b2_0 = 9.575149443481501e-02    (/ms)
    b2_1 = 9.281138012170398e-02    (/mV)

    a3_0 = 7.669829640279345e+01    (/ms)
    a3_1 = 5.374324331056838e-02    (/mV) 

    b3_0 = 1.248791525464647e+00    (/ms)
    b3_1 = 3.115037791363419e-02    (/mV)

    bh_0 = 3.573645069880386e+00    (/ms)
    bh_1 = 1.933213300303968e-01

    bh_2 = 7.496541077890667e-02    (/mV)

    ah_0 = 6.882666625638676e+00    (/ms)
    ah_1 = 4.654019001523467e+03

    ah_2 = 2.958332680760088e-02    (/mV)

    vShift = 10            	        (mV)    : shift to the right to account for Donnan potentials
	                                        : 10 mV for cclamp, 0 for oo-patch vclamp simulations

    vShift_inact = 10      	        (mV) 	: global additional shift to the right for inactivation
									        : 10 mV for cclamp, 0 for oo-patch vclamp simulations

    vShift_inact_local = 0 	        (mV) 	: additional shift to the right for inactivation, used as local range variable

    maxrate = 8.00e+03     	        (/ms)	: limiting value for reaction rates									
									        : See Patlak, 1991
	temp = 23				        (degC)	: original temp 
	q10  = 2.3						        : temperature sensitivity
	q10h = 2.3						        : temperature sensitivity for inactivation
	celsius					        (degC)

    v           (mV)
    ena         (mV)
    gna         (millimho/cm2)
    ina         (milliamp/cm2)
    ina_inax    (milliamp/cm2)      : to monitor the current 
    a1          (/ms)
    b1          (/ms)
    a2          (/ms)
    b2          (/ms)
    a3          (/ms)
    b3          (/ms)
    ah          (/ms)
    bh          (/ms)

STATE { c1 c2 c3 i1 i2 i3 i4 o }

    SOLVE kin METHOD sparse

    gna = gbar*o

:   ina = g*(v - ena)*(1e-3)
    ina = gna*(v - ena)*(1e-4) 	        : define  gbar as pS/um2 instead of mllimho/cm2
    ina_inax = gna*(v - ena)*(1e-4) 	: define  gbar as pS/um2 instead of mllimho/cm2   : to monitor



    ~ c1 <-> c2 (a1, b1)
    ~ c2 <-> c3 (a2, b2)
    ~ c3 <-> o (a3, b3)
    ~ i1 <-> i2 (a1, b1)
    ~ i2 <-> i3 (a2, b2)
    ~ i3 <-> i4 (a3, b3)
    ~ i1 <-> c1 (ah, bh)
    ~ i2 <-> c2 (ah, bh)
    ~ i3 <-> c3 (ah, bh)
    ~ i4 <-> o  (ah, bh)

    CONSERVE c1 + c2 + c3 + i1 + i2 + i3 + i4 + o = 1

: FUNCTION_TABLE tau1(v(mV)) (ms)

: FUNCTION_TABLE tau2(v(mV)) (ms)

PROCEDURE rates(v(millivolt)) {

    vS = v-vShift
    tadj = q10^((celsius - temp)/10)

    tadjh = q10h^((celsius - temp)/10)

    : maxrate = tadj*maxrate
	a1 = tadj*a1_0*exp(a1_1*vS)
	a1 = a1*maxrate/(a1+maxrate)

	b1 = tadj*b1_0*exp(-b1_1*vS)
	b1 = b1*maxrate/(b1+maxrate)

    a2 = tadj*a2_0*exp( a2_1*vS)
	a2 = a2*maxrate / (a2+maxrate)
	b2 = tadj*b2_0*exp(-b2_1*vS)
	b2 = b2*maxrate / (b2+maxrate)
    a3 = tadj*a3_0*exp( a3_1*vS)
	a3 = a3*maxrate / (a3+maxrate)
	b3 = tadj*b3_0*exp(-b3_1*vS)
	b3 = b3*maxrate / (b3+maxrate)

    bh = tadjh*bh_0/(1+bh_1*exp(-bh_2*(vS-vShift_inact-vShift_inact_local)))
	bh = bh*maxrate / (bh+maxrate)

	ah = tadjh*ah_0/(1+ah_1*exp( ah_2*(vS-vShift_inact-vShift_inact_local)))
	ah = ah*maxrate / (ah+maxrate)

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