: 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 nais
    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
    THREADSAFE
}

UNITS { (mV) = (millivolt) }

: Initialize parameters

PARAMETER {

:   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)
}

ASSIGNED {
    
    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)
    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_inax = 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)
}