: 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)

NEURON {

    SUFFIX na
    USEION na READ ena WRITE ina
    GLOBAL vShift, vShift_inact, maxrate
    RANGE vShift_inact_local
    RANGE gna, gbar, ina_ina
    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
    THREADSAFE
}

UNITS { (mV) = (millivolt) }

: initialize parameters

PARAMETER {

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

    a1_0 = 4.584982656184167e+01    (/ms)
    a1_1 = 2.393541665657613e-02    (/mV) 

    b1_0 = 1.440952344322651e-02    (/ms)
    b1_1 = 8.847609128769419e-02    (/mV)

    a2_0 = 1.980838207143563e+01    (/ms)
    a2_1 = 2.217709530008501e-02    (/mV) 

    b2_0 = 5.650174488683913e-01    (/ms)
    b2_1 = 6.108403283302217e-02    (/mV)

    a3_0 = 7.181189201089192e+01    (/ms)
    a3_1 = 6.593790601261940e-02    (/mV) 

    b3_0 = 7.531178253431512e-01    (/ms)
    b3_1 = 3.647978133116471e-02    (/mV)

    bh_0 = 2.830146966213825e+00    (/ms)
    bh_1 = 2.890045633775495e-01
    bh_2 = 6.960300544163878e-02    (/mV)

    ah_0 = 5.757824421450554e-01    (/ms)
    ah_1 = 1.628407420157048e+02
    ah_2 = 2.680107016756367e-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)
}

ASSIGNED {

    v               (mV)
    ena             (mV)
    gna             (millimho/cm2)
    ina             (milliamp/cm2)
    ina_ina         (milliamp/cm2)      : to monitor
    a1              (/ms)
    b1              (/ms)
    a2              (/ms)
    b2              (/ms)
    a3              (/ms)
    b3              (/ms)
    ah              (/ms)
    bh              (/ms)
	tadj
	tadjh
}


STATE { c1 c2 c3 i1 i2 i3 i4 o }


BREAKPOINT {

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

}


INITIAL { SOLVE kin STEADYSTATE sparse }


KINETIC kin {

    rates(v)

    ~ 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)) { 

    LOCAL vS
    
    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)
}