A multilayer cortical model to study seizure propagation across microdomains (Basu et al. 2015)

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Accession:206238
A realistic neural network was used to simulate a region of neocortex to obtain extracellular LFPs from ‘virtual micro-electrodes’ and produce test data for comparison with multisite microelectrode recordings. A model was implemented in the GENESIS neurosimulator. A simulated region of cortex was represented by layers 2/3, 5/6 (interneurons and pyramidal cells) and layer 4 stelate cells, spaced at 25 µm in each horizontal direction. Pyramidal cells received AMPA and NMDA inputs from neighboring cells at the basal and apical dendrites. The LFP data was generated by simulating 16-site electrode array with the help of ‘efield’ objects arranged at the predetermined positions with respect to the surface of the simulated network. The LFP for the model is derived from a weighted average of the current sources summed over all cellular compartments. Cell models were taken from from Traub et al. (2005) J Neurophysiol 93(4):2194-232.
References:
1 . Basu I, Kudela P, Korzeniewska A, Franaszczuk PJ, Anderson WS (2015) A study of the dynamics of seizure propagation across micro domains in the vicinity of the seizure onset zone. J Neural Eng 12:046016 [PubMed]
2 . Basu I, Kudela P, Anderson WS (2014) Determination of seizure propagation across microdomains using spectral measures of causality. Conf Proc IEEE Eng Med Biol Soc 2014:6349-52 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism: Neocortex;
Cell Type(s): Neocortex U1 L2/6 pyramidal intratelencephalic GLU cell; Neocortex U1 L5B pyramidal pyramidal tract GLU cell; Thalamus reticular nucleus GABA cell; Neocortex spiking low threshold (LTS) neuron; Neocortex spiking regular (RS) neuron; Neocortex layer 2-3 interneuron; Neocortex layer 5 interneuron;
Channel(s): I Na,p; I Na,t; I K; I A; I M; I h; I K,Ca; I A, slow; I L high threshold; I T low threshold; I Calcium;
Gap Junctions: Gap junctions;
Receptor(s): AMPA; GabaA; NMDA;
Gene(s):
Transmitter(s): Glutamate; Gaba; Amino Acids;
Simulation Environment: GENESIS;
Model Concept(s): Activity Patterns; Epilepsy;
Implementer(s): Anderson, WS ; Kudela, Pawel ;
Search NeuronDB for information about:  Thalamus reticular nucleus GABA cell; Neocortex U1 L5B pyramidal pyramidal tract GLU cell; Neocortex U1 L2/6 pyramidal intratelencephalic GLU cell; GabaA; AMPA; NMDA; I Na,p; I Na,t; I L high threshold; I T low threshold; I A; I K; I M; I h; I K,Ca; I Calcium; I A, slow; Amino Acids; Gaba; Glutamate;
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BasuEtAl2015
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ModelDescription.pdf
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P6RSd_P6RSc.g
P6RSd_P6RSd.g
P6RSd_P6RSd_Gap.g
P6RSd_raninput.g
P6RSd_ST4RS.g
P6RSd_synapsedefs.g
P6RSd_TCR.g
P6RSdcell3Dpk.p
P6RSdchanpk.g
P6RSdprotodefs.g
P6RSsyncond.g
pgenesis_command
protodefs.g
protospikeB23FS.g
protospikeB5FS.g
protospikeC23FS.g
protospikeC5FS.g
protospikeI23LTS.g
protospikeI5LTS.g
protospikenRT.g
protospikeP23FRBa.g
protospikeP23RSa.g
protospikeP23RSb.g
protospikeP23RSc.g
protospikeP23RSd.g
protospikeP5IBa.g
protospikeP5IBb.g
protospikeP5IBc.g
protospikeP5IBd.g
protospikeP5RSa.g
protospikeP6RSa.g
protospikeP6RSb.g
protospikeP6RSc.g
protospikeP6RSd.g
protospikeST4RS.g
protospikeTCR.g
randominputdefs.g
spikedefs.g
ST4RS.g
ST4RS_B23FS.g
ST4RS_B5FS.g
ST4RS_C23FS.g
ST4RS_C5FS.g
ST4RS_I23LTS.g
ST4RS_I5LTS.g
ST4RS_P23FRBa.g
ST4RS_P23RSa.g
ST4RS_P23RSb.g
ST4RS_P23RSc.g
ST4RS_P23RSd.g
ST4RS_P5IBa.g
ST4RS_P5IBb.g
ST4RS_P5IBc.g
ST4RS_P5IBd.g
ST4RS_P5RSa.g
ST4RS_P6RSa.g
ST4RS_P6RSb.g
ST4RS_P6RSc.g
ST4RS_P6RSd.g
ST4RS_raninput.g
ST4RS_ST4RS.g
ST4RS_ST4RS_Gap.g
ST4RS_synapsedefs.g
ST4RScell3Dpk.p
ST4RSchanpk.g
ST4RSprotodefs.g
ST4RSsyncond.g
synapticdelays.g *
synapticprobsTraub.g
synchansB23FS.g *
synchansB5FS.g *
synchansC23FS.g *
synchansC5FS.g *
synchansI23LTS.g *
synchansI5LTS.g *
synchansnRT.g *
synchansP23FRBa.g *
synchansP23RSa.g *
synchansP23RSb.g *
synchansP23RSc.g *
synchansP23RSd.g *
synchansP5IBa.g *
synchansP5IBb.g *
synchansP5IBc.g *
synchansP5IBd.g *
synchansP5RSa.g *
synchansP6RSa.g *
synchansP6RSb.g *
synchansP6RSc.g *
synchansP6RSd.g *
synchansSPIKEs.g *
synchansSPIKEs_base.g
synchansST4RS.g
synchansTCR.g *
syncond.g
syncond2.g
TCR.g
TCR_B23FS.g
TCR_B5FS.g
TCR_C23FS.g
TCR_C5FS.g
TCR_nRT.g
TCR_P23FRBa.g
TCR_P23RSa.g
TCR_P23RSb.g
TCR_P23RSc.g
TCR_P23RSd.g
TCR_P5IBa.g
TCR_P5IBb.g
TCR_P5IBc.g
TCR_P5IBd.g
TCR_P5RSa.g
TCR_P6RSa.g
TCR_P6RSb.g
TCR_P6RSc.g
TCR_P6RSd.g
TCR_raninput.g
TCR_ST4RS.g
TCR_synapsedefs.g
TCRcellpk.p
TCRchanpk.g
TCRprotodefs.g
TCRsyncond.g
                            
//genesis

/* FILE INFORMATION
** The 1991 Traub set of voltage and concentration dependent channels
** Implemented as tabchannels by : Dave Beeman
**      R.D.Traub, R. K. S. Wong, R. Miles, and H. Michelson
**	Journal of Neurophysiology, Vol. 66, p. 635 (1991)
**
** This file depends on functions and constants defined in defaults.g
** As it is also intended as an example of the use of the tabchannel
** object to implement concentration dependent channels, it has extensive
** comments.  Note that the original units used in the paper have been
** converted to SI (MKS) units.  Also, we define the ionic equilibrium 
** potentials relative to the resting potential, EREST_ACT.  In the
** paper, this was defined to be zero.  Here, we use -0.060 volts, the
** measured value relative to the outside of the cell.
*/

/* November 1999 update for GENESIS 2.2: Previous versions of this file used
   a combination of a table, tabgate, and vdep_channel to implement the
   Ca-dependent K Channel - K(C).  This new version uses the new tabchannel
   "instant" field, introduced in GENESIS 2.2, to implement an
   "instantaneous" gate for the multiplicative Ca-dependent factor in the
   conductance.   This allows these channels to be used with the fast
   hsolve chanmodes > 1.
*/

// Now updated for Traub et al. J Neurophysiol 2003;89:909-921.

// CONSTANTS
float EREST_ACT = -0.060 /* hippocampal cell resting potl */
float ENAP6RSc = 0.115 + EREST_ACT // 0.055
float EKP6RSc = -0.015 + EREST_ACT // -0.075
float ECAP6RSc = 0.140 + EREST_ACT // 0.080
float EARP6RSc = 0.025 + EREST_ACT // -0.035
float SOMA_A = 3.320e-9       // soma area in square meters

/*
For these channels, the maximum channel conductance (Gbar) has been
calculated using the CA3 soma channel conductance densities and soma
area.  Typically, the functions which create these channels will be used
to create a library of prototype channels.  When the cell reader creates
copies of these channels in various compartments, it will set the actual
value of Gbar by calculating it from the cell parameter file.
*/

//========================================================================
//                Tabchannel gNa-transient, gNa(F) 2005/03
//========================================================================

function make_NaF13
        str chanpath = "NaF13"
        if ({exists NaF13})
            return
        end
        create tabchannel NaF13

        setfield NaF13 \ 
            Ek              0.05 \
            Ik              0  \
            Xpower          3 \
            Ypower          1
        
        setfield NaF13 \
            Gbar 1875 \
            Gk              0 
        
        float tab_divs = 741
        float v_min = -0.12
        float v_max = 0.06
        float v, dv, i
            
        // X table for gate m
        float dv = ({v_max} - {v_min})/{tab_divs}
            
        call NaF13 TABCREATE X {tab_divs} {v_min} {v_max}
                
        v = {v_min}

        for (i = 0; i <= ({tab_divs}); i = i + 1)
            // tau
            float tau
            v = v * 1000 // temporarily set v to units of equation...
            if ({v - 3.5} < -30 )
                tau =  0.025 + 0.14 * { exp { {{v - 3.5} + 30} / 10} } 
            else
                tau =  0.02 + 0.145 * { exp { -1 * {{v - 3.5} + 30} / 10 } }
            end
            v = v * 0.001 // reset v
            // Set correct units of tau
            tau = tau * 0.001
            // inf
            float inf
                        
            v = v * 1000 // temporarily set v to units of equation...
            inf =  1 / { 1 + {exp { { -1 * {v - 3.5} - 38} / 10}} } 
            v = v * 0.001 // reset v

            // alpha and beta 
            
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            
            setfield NaF13 X_A->table[{i}] {alpha}
            setfield NaF13 X_B->table[{i}] {alpha + beta}
            v = v + dv

        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield NaF13 X_A->calc_mode 1 X_B->calc_mode 1
                    
        // Creating table for gate h, using name Y for it here

        float dv = ({v_max} - {v_min})/{tab_divs}
            
        call NaF13 TABCREATE Y {tab_divs} {v_min} {v_max}
                
        v = {v_min}

        for (i = 0; i <= ({tab_divs}); i = i + 1)
            
            // tau
            float tau
            v = v * 1000 // temporarily set v to units of equation...
            tau = 0.15 + 1.15 / { 1 + { exp {{ v  + 37 } / 15} } }
            v = v * 0.001 // reset v
          
            // Set correct units of tau
            tau = tau * 0.001
            // inf
                
            float inf
            v = v * 1000 // temporarily set v to units of equation...
            inf = 1 / { 1 + {exp {{ v + 62.9 } / 10.7}} }
            v = v * 0.001 // reset v

            // alpha and beta 
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            
            
            setfield NaF13 Y_A->table[{i}] {alpha}
            setfield NaF13 Y_B->table[{i}] {alpha + beta}
            v = v + dv

        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield NaF13 Y_A->calc_mode 1 Y_B->calc_mode 1
                    
end 

//========================================================================
//        Tabchannel gNa-persistent (non-inactivating), gNa(P) 2005/03
//========================================================================
function make_NaP13

        str chanpath = "NaP13"
        if ({exists NaP13})
            return
        end
        create tabchannel NaP13

        setfield NaP13 \ 
            Ek              0.05 \
            Ik              0  \
            Xpower          1
        
        setfield NaP13 \
            Gbar 1 \
            Gk              0 

        float tab_divs = 741
        float v_min = -0.12
        float v_max = 0.06
        float v, dv, i
            
        // X table for gate m
        float dv = ({v_max} - {v_min})/{tab_divs}
            
        call NaP13 TABCREATE X {tab_divs} {v_min} {v_max}
        v = {v_min}

        for (i = 0; i <= ({tab_divs}); i = i + 1)
            // tau
            float tau
                        
            v = v * 1000 // temporarily set v to units of equation...
            if (v < -40 )
                tau =  0.025 + 0.14 * {exp {{ v + 40 }/10}} 
            else
                tau =  0.02 + 0.145 * {exp {-1 * {v + 40}/ 10}}
            end
            v = v * 0.001 // reset v
            
            // Set correct units of tau
            tau = tau * 0.001
            // inf
            float inf
            // A = 1, B = -10, Vhalf = -48 in physiological units                 
            inf = 1 / ( {exp {(v + 0.048) / -0.01}} + 1)

            // alpha and beta 
            
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            
            setfield NaP13 X_A->table[{i}] {alpha}
            setfield NaP13 X_B->table[{i}] {alpha + beta}
                
            v = v + dv
        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
        setfield NaP13 X_A->calc_mode 1 X_B->calc_mode 1
end

//========================================================================
//        Tabchannel Anomalous Rectifier, gAR 2005/03
//========================================================================
function make_AR13
        str chanpath = "AR13"
        if ({exists {chanpath}})
            return
        end
        create tabchannel {chanpath}
        setfield {chanpath} \ 
            Ek              -0.035 \
            Ik              0  \
            Xpower          1
        
        setfield {chanpath} \
            Gbar 2.5 \
            Gk              0 
        
        float tab_divs = 741
        float v_min = -0.12
        float v_max = 0.06
        float v, dv, i
        // X table for gate m

        float dv = ({v_max} - {v_min})/{tab_divs}
        call {chanpath} TABCREATE X {tab_divs} {v_min} {v_max}
        v = {v_min}

        for (i = 0; i <= ({tab_divs}); i = i + 1)
            // tau
            float tau
            v = v * 1000 // temporarily set v to units of equation...
            tau = 1 /{{exp {-14.6 - {0.086 * v} }} + {exp {-1.87 + {0.07 * v}}}}
            v = v * 0.001 // reset v
            
            // Set correct units of tau
            tau = tau * 0.001
            // inf
            float inf
            // A = 1, B = 5.5, Vhalf = -75  in physiol units
           inf = 1 / ( {exp {(v + 0.075 ) / 0.0055}} + 1)
        
            // alpha & beta 
            
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            
            setfield {chanpath} X_A->table[{i}] {alpha}
            setfield {chanpath} X_B->table[{i}] {alpha + beta}
            v = v + dv

        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
        setfield {chanpath} X_A->calc_mode 1 X_B->calc_mode 1
end


//========================================================================
//                Tabchannel gK-delayed rectifier, gK(DR) 2005/03
//========================================================================
function make_KDR13
        str chanpath = "KDR13"
        if ({exists KDR13})
            return
        end
        create tabchannel KDR13

        setfield KDR13 \ 
            Ek              -0.095 \
            Ik              0  \
            Xpower          4
        
        setfield KDR13 \
            Gbar 1250 \
            Gk              0 

        float tab_divs = 741
        float v_min = -0.12
        float v_max = 0.06
        float v, dv, i
            
        // X table for gate m
        float dv = ({v_max} - {v_min})/{tab_divs}
            
        call KDR13 TABCREATE X {tab_divs} {v_min} {v_max}
                
        v = {v_min}

        for (i = 0; i <= ({tab_divs}); i = i + 1)
            
            // tau
            float tau
                        
            v = v * 1000 // temporarily set v to units of equation...
            if (v < -10 )
                tau =  0.25 + 4.35 * {exp {{ v + 10 }/10}} 
            else
                tau =  0.25 + 4.35 * {exp {{- v - 10}/ 10}}
            end
            v = v * 0.001 // reset v
            
            // Set correct units of tau
            tau = tau * 0.001
            // inf

            float inf
            // A = 1, B = -10, Vhalf = -29.5, in physiological units
            inf = 1 / ( {exp {(v + 0.0295) / -0.01}} + 1)
        
            // alpha and beta
            
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            
            setfield KDR13 X_A->table[{i}] {alpha}
            setfield KDR13 X_B->table[{i}] {alpha + beta}
            v = v + dv

        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield KDR13 X_A->calc_mode 1 X_B->calc_mode 1
end

//========================================================================
//                Tabchannel gK-transient, gK(A) 2005/03
//========================================================================
function make_KA13
        str chanpath = "KA13"
        if ({exists KA13})
            return
        end
        
        create tabchannel KA13

        setfield KA13 \ 
            Ek              -0.095 \
            Ik              0  \
            Xpower          4 \
            Ypower          1
        
        setfield KA13 \
            Gbar 300 \
            Gk              0 
    

        float tab_divs = 741
        float v_min = -0.12
        float v_max = 0.06
        float v, dv, i
            
        // X table for gate m

        float dv = ({v_max} - {v_min})/{tab_divs}
            
        call KA13 TABCREATE X {tab_divs} {v_min} {v_max}
                
        v = {v_min}

        for (i = 0; i <= ({tab_divs}); i = i + 1)
            
            // tau
            float tau
                
            v = v * 1000 // temporarily set v to units of equation...
            tau = 0.185 + 0.5 / {{exp {{ v + 35.8 }/19.7}} + {exp {{-v - 79.7}/12.7}}}
            v = v * 0.001 // reset v
            
            // Set correct units of tau
            tau = tau * 0.001
            // inf
            float inf
            // A = 1, B = -8.5, Vhalf = -60, in units: Physiological Units
            inf = 1 / ( {exp {(v + 0.06) / -0.0085}} + 1)

            // alpha and beta
            
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            
            setfield KA13 X_A->table[{i}] {alpha}
            setfield KA13 X_B->table[{i}] {alpha + beta}
            v = v + dv

        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield KA13 X_A->calc_mode 1 X_B->calc_mode 1
                    
        // Y table for gate h

        float dv = ({v_max} - {v_min})/{tab_divs}
        call KA13 TABCREATE Y {tab_divs} {v_min} {v_max}

        v = {v_min}
        for (i = 0; i <= ({tab_divs}); i = i + 1)
            // tau
            float tau

            v = v * 1000 // temporarily set v to units of equation...
            if (v < -63.0 )
                tau =  0.5 / {{exp {{ v + 46 }/5}} + {exp {{ -v - 238 }/37.5}}} 
            else
                tau =  9.5
            end
            v = v * 0.001 // reset v
            
            // Set correct units of tau
            tau = tau * 0.001
            // inf
            float inf
            // A = 1, B = 6, Vhalf = -78, in physiological units
            inf = 1 / ( {exp {(v + 0.078) / 0.006}} + 1)

            // alpha and beta
            
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            
            setfield KA13 Y_A->table[{i}] {alpha}
            setfield KA13 Y_B->table[{i}] {alpha + beta}

            v = v + dv

        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield KA13 Y_A->calc_mode 1 Y_B->calc_mode 1
end

//========================================================================
//                Tabchannel gK2-slow, gK2 2005/03
//========================================================================
function make_K213
        str chanpath = "K213"
        if ({exists K213})
            return
        end
        create tabchannel K213
        setfield K213 \ 
            Ek              -0.095 \
            Ik              0  \
            Xpower          1 \
            Ypower          1
        
        setfield K213 \
            Gbar 1 \
            Gk              0 

        float tab_divs = 741
        float v_min = -0.12
        float v_max = 0.06
        float v, dv, i
            
        // X table for gate m 
        float dv = ({v_max} - {v_min})/{tab_divs}
            
        call K213 TABCREATE X {tab_divs} {v_min} {v_max}
                
        v = {v_min}

        for (i = 0; i <= ({tab_divs}); i = i + 1)
            
            // tau
            float tau

            v = v * 1000 // temporarily set v to units of equation...
            tau = 4.95 + 0.5 / { {exp { {v - 81} / 25.6}} + {exp { {- v - 132} / 18 }}}
            v = v * 0.001 // reset v
            
            // Set correct units of tau
            tau = tau * 0.001
            // Looking at rate: inf
                

            float inf
            // A = 1, B = -17, Vhalf = -10, in physiological units
            inf = 1 / ( {exp {(v + 0.01) / -0.017}} + 1)
            
            // alpha and beta
            
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            
            setfield K213 X_A->table[{i}] {alpha}
            setfield K213 X_B->table[{i}] {alpha + beta}
                
            v = v + dv

        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield K213 X_A->calc_mode 1 X_B->calc_mode 1
                    
        // Y table for gate h
        float dv = ({v_max} - {v_min})/{tab_divs}
            
        call K213 TABCREATE Y {tab_divs} {v_min} {v_max}
                
        v = {v_min}
        for (i = 0; i <= ({tab_divs}); i = i + 1)
            
            // tau
            float tau
                
            v = v * 1000 // temporarily set v to units of equation...
            tau = 60 + 0.5 / {{exp {{ v - 1.33 }/200}} + {exp {{- v - 130}/ 7.1}}}
            v = v * 0.001 // reset v
            
            // Set correct units of tau
            tau = tau * 0.001

            //inf
            float inf
            // A = 1, B = 10.6, Vhalf = -58, in units: Physiological Units
            inf = 1 / ( {exp {(v + 0.058) / 0.0106}} + 1)

            // alpha and beta 
            
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            
            setfield K213 Y_A->table[{i}] {alpha}
            setfield K213 Y_B->table[{i}] {alpha + beta}
                
            v = v + dv

        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
        setfield K213 Y_A->calc_mode 1 Y_B->calc_mode 1
end

//========================================================================
//           Tabchannel gK-muscarinic receptor supressed, gK(M) 2005/03
//========================================================================
function make_KM13
        str chanpath = "KM13"
        if ({exists KM13})
            return
        end
        create tabchannel KM13

        setfield KM13 \ 
            Ek              -0.095 \
            Ik              0  \
            Xpower          1
        
        setfield KM13 \
            Gbar 75 \
            Gk              0 

        float tab_divs = 741
        float v_min = -0.12
        float v_max = 0.06
        float v, dv, i
            
        // Creating table for gate m, using name X for it here

        float dv = ({v_max} - {v_min})/{tab_divs}
            
        call KM13 TABCREATE X {tab_divs} {v_min} {v_max}
                
        v = {v_min}
        for (i = 0; i <= ({tab_divs}); i = i + 1)
            
            //alpha
            float alpha
            // A = 0.02, B = -5, Vhalf = -20, in units: Physiological Units
            alpha = 20 / ( {exp {(v +0.02)/-0.005}} + 1)
        
            //beta
            float beta
            // A = 0.01, B = -18, Vhalf = -43, in physiological Units
           beta = 10 * {exp {(v +0.043) / -0.018}}

            // Using the alpha and beta expressions to populate the tables
            float tau = 1/(alpha + beta)
            
            setfield KM13 X_A->table[{i}] {alpha}
            setfield KM13 X_B->table[{i}] {alpha + beta}
            v = v + dv

        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield KM13 X_A->calc_mode 1 X_B->calc_mode 1
end

//========================================================================
//          Tabchannel gCa(L)-low threshold, transient, gCa(L) 2005/03
//========================================================================
function make_CaL13
        str chanpath = "CaL13"
        if ({exists CaL13})
            return
        end
        
        create tabchannel CaL13
        setfield CaL13 \ 
            Ek              0.125 \
            Ik              0  \
            Xpower          2 \
            Ypower          1
        
        setfield CaL13 \
            Gbar 1 \
            Gk              0 

        
        float tab_divs = 741
        float v_min = -0.12
        float v_max = 0.06
        float v, dv, i
            
        // Creating table for gate m, using name X for it here

        float dv = ({v_max} - {v_min})/{tab_divs}
            
        call CaL13 TABCREATE X {tab_divs} {v_min} {v_max}
                
        v = {v_min}

        for (i = 0; i <= ({tab_divs}); i = i + 1)
            
            // Looking at rate: tau
            float tau
                        
            v = v * 1000 // temporarily set v to units of equation...
            tau = 0.204 + 0.333 / { {exp {{15.8 + v} / 18.2 }} + {exp {{- v - 131} / 16.7}} }
            v = v * 0.001 // reset v
            
            // Set correct units of tau
            tau = tau * 0.001
            // inf
            float inf
            // A = 1, B = -6.2, Vhalf = -56.0, in physiological Units
            inf = 1 / ( {exp {(v + 0.056) / -0.0062}} + 1)
        
            // alpha and beta 
            
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            
            setfield CaL13 X_A->table[{i}] {alpha}
            setfield CaL13 X_B->table[{i}] {alpha + beta}
            v = v + dv

        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield CaL13 X_A->calc_mode 1 X_B->calc_mode 1
                    
        // Creating table for gate h, using name Y for it here

        float dv = ({v_max} - {v_min})/{tab_divs}
            
        call CaL13 TABCREATE Y {tab_divs} {v_min} {v_max}
                
        v = {v_min}

        for (i = 0; i <= ({tab_divs}); i = i + 1)
            // tau
            float tau

            v = v * 1000 // temporarily set v to units of equation...
            if (v < -81.0 )
                tau =  0.333 * {exp {{ v + 466 } / 66.6}} 
            else
                tau =  9.32 + 0.333 * {exp {{ - v - 21 } / 10.5}}
            end
            v = v * 0.001 // reset v
            
            // Set correct units of tau
            tau = tau * 0.001
            //inf

            float inf
            // A = 1, B = 4, Vhalf = -80, in units: Physiological Units
            inf = 1 / ( {exp {(v + 0.08 ) / 0.004}} + 1)
        

            // alpha and beta 
            
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            
            setfield CaL13 Y_A->table[{i}] {alpha}
            setfield CaL13 Y_B->table[{i}] {alpha + beta}
            v = v + dv

        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield CaL13 Y_A->calc_mode 1 Y_B->calc_mode 1
end

//==========================================================================
//            Tabchannel gCaH-high threshold calcium, gCa(L) "long" 2003/05
//==========================================================================
function make_CaH13
        str chanpath = "CaH13"
        if ({exists CaH13})
            return
        end
        create tabchannel CaH13
        setfield CaH13 \ 
            Ek              0.125 \
            Ik              0  \
            Xpower          2
        
        setfield CaH13 \
            Gbar 5 \
            Gk              0 

        float tab_divs = 741
        float v_min = -0.12

        float v_max = 0.06
        float v, dv, i
        // Creating table for gate m, using name X for it here

        float dv = ({v_max} - {v_min})/{tab_divs}
            
        call CaH13 TABCREATE X {tab_divs} {v_min} {v_max}
                
        v = {v_min}

        for (i = 0; i <= ({tab_divs}); i = i + 1)
            
            // alpha
            float alpha

            // A = 1.6, B = -13.888889, Vhalf = 5, in physiological Units
            alpha = 1600 / ( {exp {(v - 0.005) /-0.013888889000000001}} + 1)
        
            // beta
            float beta

            if ( {abs {(v + 0.0089)/ -0.005}} < 1e-6)
                beta = 100 * (1 + (v +0.0089)/-0.005/2)
            else
              beta = 100 * ((v + 0.0089 ) / -0.005) /(1 - {exp {-1 * (v + 0.0089)/-0.005}})
            end

            // Using the alpha and beta expressions to populate the tables

            float tau = 1/(alpha + beta)
            
            setfield CaH13 X_A->table[{i}] {alpha}
            setfield CaH13 X_B->table[{i}] {alpha + beta}
            v = v + dv

        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield CaH13 X_A->calc_mode 1 X_B->calc_mode 1
                    

end


//========================================================================
//             Ca conc, Traub et al. J Neurophysiol 2003;89:909-921.
//========================================================================
/****************************************************************************
Next, we need an element to take the Calcium current calculated by the Ca
channel and convert it to the Ca concentration.  The "Ca_concen" object
solves the equation dC/dt = B*I_Ca - C/tau, and sets Ca = Ca_base + C.  As
it is easy to make mistakes in units when using this Calcium diffusion
equation, the units used here merit some discussion.

With Ca_base = 0, this corresponds to Traub's diffusion equation for
concentration, except that the sign of the current term here is positive, as
GENESIS uses the convention that I_Ca is the current flowing INTO the
compartment through the channel.  In SI units, the concentration is usually
expressed in moles/m^3 (which equals millimoles/liter), and the units of B
are chosen so that B = 1/(ion_charge * Faraday * volume). Current is
expressed in amperes and one Faraday = 96487 coulombs.  However, in this
case, Traub expresses the concentration in arbitrary units, current in
microamps and uses tau = 13.33 msec (50 msec soma, 20 msec dendrites in the
2003 J Neurophys paper).  If we use the same concentration units,
but express current in amperes and tau in seconds, our B constant is then
10^12 times the constant (called "phi") used in the paper.  The actual value
used will typically be determined by the cell reader from the cell
parameter file (will vary inversely with surface area of compartment).  
However, for the prototype channel we will use Traub's
corrected value for the soma.  (An error in the paper gives it as 17,402
rather than 17.402.)  In our units, this will be 17.402e12.

****************************************************************************/
function make_Ca_s13
        str chanpath = "Ca_s13"
        if ({exists Ca_s13})
            return
        end
        create Ca_concen Ca_s13

        // Setting params for a decaying_pool_model

        setfield Ca_s13 \
            tau                   { 1.0 / 10 }    \
            Ca_base               0
        
        addfield Ca_s13 addmsg1
        setfield Ca_s13 \
                addmsg1        "../CaH13 . I_Ca Ik"
        addfield Ca_s13 addmsg2
        setfield Ca_s13 \
                addmsg2        "../CaL13 . I_Ca Ik"
end

/*
This Ca_concen element should receive an "I_Ca" message from the calcium
channel, accompanied by the value of the calcium channel current.  As we
will ordinarily use the cell reader to create copies of these prototype
elements in one or more compartments, we need some way to be sure that the
needed messages are established.  Although the cell reader has enough
information to create the messages which link compartments to their channels
and to other adjacent compartments, it must be provided with the information
needed to establish additional messages.  This is done by placing the
message string in a user-defined field of one of the elements which is
involved in the message.  The cell reader recognizes the added field names
"addmsg1", "addmsg2", etc. as indicating that they are to be
evaluated and used to set up messages.  The paths are relative to the
element which contains the message string in its added field.  Thus,
"../Ca_hip_traub91" refers to the sibling element Ca_hip_traub91 and "."
refers to the Ca_hip_conc element itself.
*/

/****************************************************************************/
function make_Ca_d13
        str chanpath = "Ca_d13"

        if ({exists Ca_d13})
            return
        end

        create Ca_concen Ca_d13

        // Setting params for a decaying_pool_model

        setfield Ca_d13 \
            tau                   { 1.0 / 50 }    \
            Ca_base               0
        
        addfield Ca_d13 addmsg1
        setfield Ca_d13 \
                addmsg1        "../CaH13 . I_Ca Ik"
        addfield Ca_d13 addmsg2
        setfield Ca_d13 \
                addmsg2        "../CaL13 . I_Ca Ik"
end
/*
This Ca_concen element should receive an "I_Ca" message from the calcium
channel, accompanied by the value of the calcium channel current.  As we
will ordinarily use the cell reader to create copies of these prototype
elements in one or more compartments, we need some way to be sure that the
needed messages are established.  Although the cell reader has enough
information to create the messages which link compartments to their channels
and to other adjacent compartments, it must be provided with the information
needed to establish additional messages.  This is done by placing the
message string in a user-defined field of one of the elements which is
involved in the message.  The cell reader recognizes the added field names
"addmsg1", "addmsg2", etc. as indicating that they are to be
evaluated and used to set up messages.  The paths are relative to the
element which contains the message string in its added field.  Thus,
"../Ca_hip_traub91" refers to the sibling element Ca_hip_traub91 and "."
refers to the Ca_hip_conc element itself.
*/

//===============================================================================
//  Ca-dependent K Channel - K(C) - (vdep_channel with table and tabgate)2005/03
//===============================================================================
/*
The expression for the conductance of the potassium C-current channel has a
typical voltage and time dependent activation gate, where the time dependence
arises from the solution of a differential equation containing the rate
parameters alpha and beta.  It is multiplied by a function of calcium
concentration that is given explicitly rather than being obtained from a
differential equation.  Therefore, we need a way to multiply the activation
by a concentration dependent value which is determined from a lookup table.
This is accomplished by using the Z gate with the new tabchannel "instant"
field, introduced in GENESIS 2.2, to implement an "instantaneous" gate for
the multiplicative Ca-dependent factor in the conductance.
*/

function make_KCs13
        if ({exists KCs13})
            return
        end
        
        create tabchannel KCs13

        setfield KCs13 \ 
            Ek              -0.095 \
            Ik              0  \
            Xpower          1 \
            Zpower          1
            
        setfield KCs13 \
            Gbar 120 \
            Gk              0 

        float tab_divs = 1041
        float v_min = -0.12
        float v_max = 0.14

        float v, dv, i
        // Creating table for gate m, using name X for it here
        float dv = ({v_max} - {v_min})/{tab_divs}
            
        call KCs13 TABCREATE X {tab_divs} {v_min} {v_max}
                
        v = {v_min}

        for (i = 0; i <= ({tab_divs}); i = i + 1)
            // Looking at rate: alpha
            float alpha
            v = v * 1000 // temporarily set v to units of equation...

            if (v < -10 )
                alpha =  {2 / 37.95} * { exp { {{v + 50 } / 11} - {{ v + 53.5} / 27} } } 
            else
                alpha =  2 * {exp { { {-1 * v} - 53.5 } / 27 }}
            end
            v = v * 0.001 // reset v
            
            // Set correct units of alpha
            alpha = alpha * 1000

            // beta
            float beta
                        
            v = v * 1000 // temporarily set v to units of equation...
            // Equation depends on alpha, so converting it...
            alpha = alpha * 0.001
            if (v < -10 )
                beta =  2 * {exp { { {-1 * v} - 53.5 } / 27 }} - alpha 
            else
                beta =  0.0
            end
            v = v * 0.001 // reset v
            alpha = alpha * 1000  // resetting alpha
                        
            // Set correct units of beta
            beta = beta * 1000

            // Using the alpha and beta expressions to populate the tables
            float tau = 1/(alpha + beta)
            setfield KCs13 X_A->table[{i}] {alpha}
            setfield KCs13 X_B->table[{i}] {alpha + beta}
            v = v + dv

        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield KCs13 X_A->calc_mode 1 X_B->calc_mode 1
                    
        // Adding voltage independent concentration term
        
        float conc_min = 0
        float conc_max = 1000
        float dc = ({conc_max} - {conc_min})/{tab_divs}
        float ca_conc = {conc_min}
        
        call KCs13 TABCREATE  Z {tab_divs} {conc_min} {conc_max}
        float const_state

        for (i = 0; i <= ({tab_divs}); i = i + 1)
                
            // Equation is in different set of units...
            ca_conc = ca_conc * 0.000001

            if (ca_conc < 0.00025 )
                const_state =  {ca_conc / 0.00025} 
            else
                const_state =  1
            end
            // Converting back...
            ca_conc = ca_conc * 1000000
            
            setfield KCs13 Z_A->table[{i}] {0}
            setfield KCs13 Z_B->table[{i}] {const_state}
            
            ca_conc= ca_conc + dc
        end
             
        tweaktau KCs13 Z
        
        addfield KCs13 addmsg1
        setfield KCs13 addmsg1  "../Ca_s13  . CONCEN Ca"
end

function make_KCd13

        if ({exists KCd13})
            return
        end
        create tabchannel KCd13
            
        setfield KCd13 \ 
            Ek              -0.095 \
            Ik              0  \
            Xpower          1 \
            Zpower          1
            
        
        setfield KCd13 \
            Gbar 120 \
            Gk              0 

        float tab_divs = 1041
        float v_min = -0.12

        float v_max = 0.14

        float v, dv, i
            
        // Creating table for gate m, using name X for it here

        float dv = ({v_max} - {v_min})/{tab_divs}
            
        call KCd13 TABCREATE X {tab_divs} {v_min} {v_max}
                
        v = {v_min}

            

        for (i = 0; i <= ({tab_divs}); i = i + 1)
            
            // Looking at rate: alpha
                

            float alpha

            v = v * 1000 // temporarily set v to units of equation...
            if (v < -10 )
                alpha =  {2 / 37.95} * { exp { {{v + 50 } / 11} - {{ v + 53.5} / 27} } } 
            else
                alpha =  2 * {exp { { {-1 * v} - 53.5 } / 27 }}
            end
            v = v * 0.001 // reset v
            
            // Set correct units of alpha
            alpha = alpha * 1000
            
            // Looking at rate: beta
            float beta
                        
            v = v * 1000 // temporarily set v to units of equation...
            // Equation depends on alpha, so converting it...
            alpha = alpha * 0.001

            if (v < -10 )
                beta =  2 * {exp { { {-1 * v} - 53.5 } / 27 }} - alpha 
            else
                beta =  0.0
            end
            v = v * 0.001 // reset v
            alpha = alpha * 1000  // resetting alpha
                        
            // Set correct units of beta
            beta = beta * 1000

            // Using the alpha and beta expressions to populate the tables

            float tau = 1/(alpha + beta)
            
            setfield KCd13 X_A->table[{i}] {alpha}
            setfield KCd13 X_B->table[{i}] {alpha + beta}
                    
            v = v + dv

        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield KCd13 X_A->calc_mode 1 X_B->calc_mode 1
                    
        // Adding voltage independent concentration term
        
        float conc_min = 0
        float conc_max = 1000

        float dc = ({conc_max} - {conc_min})/{tab_divs}

        float ca_conc = {conc_min}
        
        call KCd13 TABCREATE  Z {tab_divs} {conc_min} {conc_max}
        
        float const_state

        for (i = 0; i <= ({tab_divs}); i = i + 1)
        
            // Equation is in different set of units...
            ca_conc = ca_conc * 0.000001

            if (ca_conc < 0.00025 )
                const_state =  {ca_conc / 0.00025} 
            else
                const_state =  1
            end
        
            // Converting back...
            ca_conc = ca_conc * 1000000
            
            setfield KCd13 Z_A->table[{i}] {0}
            setfield KCd13 Z_B->table[{i}] {const_state}
            
            ca_conc= ca_conc + dc
            
        end
        tweaktau KCd13 Z
        
        addfield KCd13 addmsg1
        setfield KCd13 addmsg1  "../Ca_d13  . CONCEN Ca"

end


//========================================================================
//             Tabulated Ca-dependent K AHP Channel,gK(AHP) 2003/05
//========================================================================

/* This is a tabchannel which gets the calcium concentration from Ca_hip_conc
   in order to calculate the activation of its Z gate.  It is set up much
   like the Ca channel, except that the A and B tables have values which are
   functions of concentration, instead of voltage.
*/
function make_KAHPs13

        if ({exists KAHPs13})
            return
        end
        create tabchannel KAHPs13
        setfield KAHPs13 \ 
            Ek              -0.095 \
            Ik              0  \
            Zpower          1
        
        setfield KAHPs13 \
            Gbar 1 \
            Gk              0 
        float tab_divs = 1041

        // Channel is dependent on concentration of: Calcium, rate equations will involve variable: ca_conc
        float c
        float conc_min = 0
        float conc_max = 1000

        float dc = ({conc_max} - {conc_min})/{tab_divs}

        float ca_conc = {conc_min}
            
        call KAHPs13 TABCREATE Z {tab_divs} {conc_min} {conc_max}
            

        for (c = 0; c <= ({tab_divs}); c = c + 1)
                    
            // Looking at rate: alpha
            float alpha
            float v    
            v = v * 1000 // temporarily set v to units of equation...
           // Equation depends on concentration, so converting that too... 
            ca_conc = ca_conc * 0.000001

            if (ca_conc < 0.0001 )
                alpha =  ca_conc/0.01 
            else
                alpha =  0.01
            end
            v = v * 0.001 // reset v
            ca_conc = ca_conc * 1000000 // resetting ca_conc 
            
            // Set correct units of alpha
            alpha = alpha * 1000
            
            // Looking at rate: beta
            float beta
                        
            v = v * 1000 // temporarily set v to units of equation...
           // Equation depends on concentration, so converting that too... 
            ca_conc = ca_conc * 0.000001
            beta = 0.001
            v = v * 0.001 // reset v
            ca_conc = ca_conc * 1000000 // resetting ca_conc 
            
            // Set correct units of beta
            beta = beta * 1000
            
            // Using the alpha and beta expressions to populate the tables
            float tau = 1/(alpha + beta)
            
            setfield KAHPs13 Z_A->table[{c}] {alpha}
            setfield KAHPs13 Z_B->table[{c}] {alpha + beta}
                    ca_conc = ca_conc + dc
                
        end // end of for (c = 0; c <= ({tab_divs}); c = c + 1)
                
        setfield KAHPs13 Z_conc 1
        setfield KAHPs13 Z_A->calc_mode 1 Z_B->calc_mode 1
                    
// Use an added field to tell the cell reader to set up the
// CONCEN message from the Ca_concen element
        addfield KAHPs13 addmsg1
        setfield KAHPs13  \
                addmsg1        "../Ca_s13 . CONCEN Ca"

end


function make_KAHPd13

        if ({exists KAHPd13})
            return
        end
        create tabchannel KAHPd13
        setfield KAHPd13 \ 
            Ek              -0.095 \
            Ik              0  \
            Zpower          1
        
        setfield KAHPd13 \
            Gbar 1 \
            Gk              0 

        float tab_divs = 1041

        // Channel is dependent on concentration of: Calcium, rate equations will involve variable: ca_conc
        float c
        float conc_min = 0
        float conc_max = 1000

        float dc = ({conc_max} - {conc_min})/{tab_divs}
        float ca_conc = {conc_min}
            
        call KAHPd13 TABCREATE Z {tab_divs} {conc_min} {conc_max}

        for (c = 0; c <= ({tab_divs}); c = c + 1)
            // Looking at rate: alpha
                
            float alpha
            float v    

           v = v * 1000 // temporarily set v to units of equation... 
           // Equation depends on concentration, so converting that too... 
            ca_conc = ca_conc * 0.000001

            if (ca_conc < 0.0001 )
                alpha =  ca_conc/0.01 
            else
                alpha =  0.01
            end
            
            v = v * 0.001 // reset v
            ca_conc = ca_conc * 1000000 // resetting ca_conc 
            
            // Set correct units of alpha
            alpha = alpha * 1000
            
            // Looking at rate: beta
            float beta
                
            v = v * 1000 // temporarily set v to units of equation...
           // Equation depends on concentration, so converting that too... 
            ca_conc = ca_conc * 0.000001

            beta = 0.001
            
            v = v * 0.001 // reset v
            ca_conc = ca_conc * 1000000 // resetting ca_conc 
            
            // Set correct units of beta
            beta = beta * 1000
            
            // Using the alpha and beta expressions to populate the tables
            float tau = 1/(alpha + beta)
            
            setfield KAHPd13 Z_A->table[{c}] {alpha}
            setfield KAHPd13 Z_B->table[{c}] {alpha + beta}
                    ca_conc = ca_conc + dc
                
        end // end of for (c = 0; c <= ({tab_divs}); c = c + 1)
                
        setfield KAHPd13 Z_conc 1
        setfield KAHPd13 Z_A->calc_mode 1 Z_B->calc_mode 1
                    
// Use an added field to tell the cell reader to set up the
// CONCEN message from the Ca_concen element
        addfield KAHPd13 addmsg1
        setfield KAHPd13  \
                addmsg1        "../Ca_d13 . CONCEN Ca"
end


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