traub.hoc

/*
Traub CA3 compartmental model

*/

// the variable figNumber is defined in each GenerateFigX.hoc file
// divide both gKahp and gKc conductances by 20 as per the legend of Fig. 4 in Traub et al. 1991
if ( figNumber == 4 ) { scaleFactor = 20 } else { scaleFactor = 1 }

/* 

***Note on the CaShell mechanism***

This mechanism implements the Ca dynamics of the Traub model according to

d xi_i / dt = -phi_i I_Ca,i - beta_xi xi_i

where xi_i is the calcium concentration variable (dimensionless), 
phi_i is a compartment-dependent conversion factor for the Ca current to 
calcium concentration change, and beta_xi is a time constant of calcium 
clearance. 

In the Traub model, the current is in units of nA, time is in units of ms. 
So the units of phi_i are 1/(ms nA). In NEURON, time is in units of ms, 
but current is in units of mA/cm^2. So we need to convert the current to
units of nA. For this we compute the surface area (S_A) of the compartment,
S_A_um2 = pi * diam * L, in units of um^2. Since 1 um = 10^-4 cm, we multiply
by 10^-8 to obtain S_A_cm2 in units of cm^2. If we multiply I_Ca,i (NEURON) by 
S_A_cm2, we obtain the current in units of mA. To convert to nA, we need to 
multiply by 1 mA = 10^6 nA. Hence,

phi_i (Traub) * I_Ca,i (Traub) = phi_i (Traub) * I_Ca,i (NEURON) * S_A_cm2 * 10^6 (mA to nA) 

Therefore the ph_i constant in NEURON is given by 

phi_i (NEURON) = phi_i (Traub) * S_A_cm2 * 10^6 = phi_i (Traub) * S_A_um2 * 10^-8 * 10^6
phi_i (NEURON) = phi_i (Traub) * S_A_um2 * 10^-2

Traub et al. (1991) phi_i values:

phi_9 = 17,402 (our soma, use 17.402)
phi_1 to phi_7 = 7,769 (our basal[7] to basal[1], use 7.769)
phi_8 = 34,530 (our basal[0], use 34.530)
phi_10 = 26,404 (our apical[0], use 26.404)
phi_11 to phi_19 = 5,941 (our apical[1] to apical[9], use 5.941)

Note: as explained in Traub et al. (1994), these values are wrong by a factor 
1,000 and should be replaced by the ones in parentheses.

Since there are no gCa in basal[7] and in apical[9], there is 
no need to insert CaShell there. We compute the NEURON values 
immediately below.
*/

//Set resting membrane potential to 0 mV
v_init = 0

rss_gCa=0

//Set Initial Ca level
cai0_CaShell=0

diam_soma = 4.23 * 2  // from Methods of Traub 1991, radius = 4.23 um 
L_soma = 125  // um

phi_soma_traub_corrected = 17.402
phi_soma = phi_soma_traub_corrected * PI * diam_soma * L_soma * 1e-2

diam_basal = 2.42 * 2  // according to Traub 1991 radius = 2.42 um
L_basal = 110.0  // um

phi_basal_1_6_traub_corrected = 7.769 
phi_basal_1_6 = phi_basal_1_6_traub_corrected * PI * diam_basal * L_basal * 1e-2

phi_basal_0_traub_corrected = 34.530 
phi_basal_0 = phi_basal_0_traub_corrected * PI * diam_basal * L_basal * 1e-2

// these morphology values give a smaller area than reported in the paper
// (2.8935 µm radius and 120.35 µm length give 2188 um2 area)
diam_apical = 2.89 * 2  // according to Traub 1991 radius = 2.89 um
L_apical = 120  // um

phi_apical_0_traub_corrected = 26.404
phi_apical_0 = phi_apical_0_traub_corrected * PI * diam_apical * L_apical * 1e-2

phi_apical_1_8_traub_corrected = 5.941
phi_apical_1_8 = phi_apical_1_8_traub_corrected * PI * diam_apical * L_apical * 1e-2

// Reversal potentials for the different ions
ek_rev = -15
ena_rev = 115
eca_rev = 140

// Now create model compartments 
create soma

create basal[8]
create apical[10]

//setup topology
connect apical[0](0), soma(1) //child, parent
connect basal[0](0), soma(0)

if ( figNumber != 4 ) {
//connect basal dendrites in chain order to soma
for i = 1, 7 {
    connect basal[i](0), basal[i-1](1) // child, parent
}

// As above, results in apical[9](0) -> apical[8](1) -> apical[8](0) -> ... apical[1](0) -> apical[0](1)
// where we use the notation " child -> parent" to denote child compartment connected to 
// parent compartment
for i = 1, 9 {
    connect apical[i](0), apical[i-1](1) // child, parent
}
}

Cm_t = 3  // uF/cm^2
Ra_t = 100  // Ohm cm
gm_t = 1/10000  // S/cm^2
ep_t = 0  // mV

// Setup all conductances in soma
soma { //
    nseg = 1
    diam = diam_soma
    L = L_soma
    Ra=Ra_t
    cm=Cm_t
    
    insert pas
    e_pas= ep_t
    g_pas = gm_t // in units of S/cm^2
    
    insert gNa
    gmax_gNa = 0.03
    
    insert gKdr
    gmax_gKdr = 0.015
    
    insert gKa
    gmax_gKa = 0.005
    
    insert gCa
    gmax_gCa = 0.004
        
    insert CaShell
    phi_CaShell = phi_soma 
    
    // divide both gKahp and gKc conductances by 20 as per the legend of Fig. 4 in Traub et al. 1991
    insert gKahp
    gmax_gKahp = 0.0008/scaleFactor 
    
    insert gKc
    gmax_gKc = 0.010/scaleFactor
    
    //compartment ions: Na, K, Ca 
    ena = ena_rev
    ek = ek_rev
    eca = eca_rev

    // this following allows cai/cao to be state variables and eca to be a parameter
    // needs to be at end of insertion process not to be overridden by other
    // Ca related mechanism insertions
    ion_style("ca_ion",3,1,0,0,0)   
}

// Setup basic passive parameters in basal and apical compartments
for i = 0, 7 {
    basal[i] {    
	Ra=Ra_t
	cm=Cm_t
	insert pas
	e_pas= ep_t
	g_pas = gm_t
	nseg = 1
	diam = diam_basal 
	L = L_basal 
    }
}

for i = 0, 9 {
    apical[i] { 
        Ra=Ra_t
	cm=Cm_t
	insert pas
	e_pas= ep_t
	g_pas = gm_t
	nseg = 1
	diam = diam_apical
	L = L_apical
    }
}

define_shape()

// Setup active conductances in basal and apical compartments

//setup a vector containing the conductances for each basal compartement
objref gCa_basal
gCa_basal = new Vector(7, 0.0) // the last compartment has no gCa
gCa_basal.x[0] = 0.008 // S/cm^2
gCa_basal.x[1] = 0.005
gCa_basal.fill(0.012, 2, 4) // values at index 2, 3 and 4
gCa_basal.fill(0.005, 5, 6) // values at index 5 and 6

// divide both gKahp and gKc conductances by 20 as per the legend of Fig. 4 in Traub et al. 1991
objref gKahp_basal
gKahp_basal = new Vector(7, 0.0008/scaleFactor) // the last compartment has no gKahp

objref gKc_basal
gKc_basal = new Vector(7, 0.0) // the last compartment has no gKc
gKc_basal.x[0] = 0.020/scaleFactor // S/cm^2
gKc_basal.x[1] = 0.005/scaleFactor
gKc_basal.fill(0.010/scaleFactor, 2, 4) // values at index 2, 3 and 4
gKc_basal.fill(0.005/scaleFactor, 5, 6) // values at index 5 and 6

for i = 0, 6 {
    basal[i] {
	insert gCa
	gmax_gCa = gCa_basal.x[i]
	
	insert CaShell
	if ( i == 0 ) {
	    phi_CaShell = phi_basal_0
	} else {
	    phi_CaShell = phi_basal_1_6 
	}
	
	insert gKahp
	gmax_gKahp = gKahp_basal.x[i]
	
	insert gKc
	gmax_gKc = gKc_basal.x[i]
	
	// Compartment ions: Ca, K
	ek = ek_rev
	eca = eca_rev
	
	ion_style("ca_ion",3,1,0,0,0)
    }    
}

// add the gNa and gKdr conductances in the subset of basal compartments specified by Traub 1991
basal[0] {
    insert gNa
    gmax_gNa = 0.015
    
    insert gKdr
    gmax_gKdr = 0.005
    
    // Compartment ions: Na, K
    ek = ek_rev
    ena = ena_rev
}

basal[2] {
    insert gNa
    gmax_gNa = 0.020
    
    insert gKdr
    gmax_gKdr = 0.020
    
    // Compartment ions: Na, K
    ek = ek_rev
    ena = ena_rev
}

// setup a vector containing the conductances for each apical compartment
objref gCa_apical
gCa_apical = new Vector(9, 0.0) // the last compartment has no gCa
gCa_apical.x[0] = 0.008 // S/cm^2
gCa_apical.x[1] = 0.005
gCa_apical.fill(0.017, 2, 4) // values at index 2, 3 and 4
gCa_apical.fill(0.010, 5, 6) // values at index 5 and 6
gCa_apical.fill(0.005, 7, 8) // values at index 7 and 8

// divide both gKahp and gKc conductances by 20 as per the legend of Fig. 4 in Traub et al. 1991
objref gKahp_apical
gKahp_apical = new Vector(9, 0.0008/scaleFactor) // the last compartment has no gKahp

objref gKc_apical
gKc_apical = new Vector(9, 0.0) // the last compartment has no gKc
gKc_apical.x[0] = 0.020/scaleFactor // S/cm^2
gKc_apical.x[1] = 0.005/scaleFactor
gKc_apical.fill(0.015/scaleFactor, 2, 6) // values at index 2 to 6
gKc_apical.fill(0.005/scaleFactor, 7, 8) // values at index 7 and 8

for i = 0, 8 {
    apical[i] {
	insert gCa
	gmax_gCa = gCa_apical.x[i]
	
	insert CaShell
	if ( i == 0 ) {
	    phi_CaShell = phi_apical_0
	} else {
	    phi_CaShell = phi_apical_1_8
	}
	
	insert gKahp
	gmax_gKahp = gKahp_apical.x[i]
	
	insert gKc
	gmax_gKc = gKc_apical.x[i]
	
	// Compartment ions: Ca, K
	ek = ek_rev
	eca = eca_rev

	ion_style("ca_ion",3,1,0,0,0)
    }    
}

// add the gNa and gKdr conductances in the subset of apical compartments specified by Traub 1991
apical[0] {
    insert gNa
    gmax_gNa = 0.015
    
    insert gKdr
    gmax_gKdr = 0.005
    
    // Compartment ions: Na, K
    ek = ek_rev
    ena = ena_rev

}

apical[2] {
    insert gNa
    gmax_gNa = 0.020
    
    insert gKdr
    gmax_gKdr = 0.020
    
    // Compartment ions: Na, K
    ek = ek_rev
    ena = ena_rev
    
}