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 ENAP23RSb = 0.115 + EREST_ACT // 0.055
float EKP23RSb = -0.015 + EREST_ACT // -0.075
float ECAP23RSb = 0.140 + EREST_ACT // 0.080
float EARP23RSb = 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_NaF2
        str chanpath = "NaF2"
        if ({exists NaF2})
            return
        end
        create tabchannel NaF2
        setfield NaF2 \ 
            Ek              0.05 \
            Ik              0  \
            Xpower          3 \
            Ypower          1
        setfield NaF2 \
            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 NaF2 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 // v to units of equation
            if (v  < -26.5 )
                tau =  0.025 + 0.14 * { exp { {v  + 26.5} / 10} } 
            else
                tau =  0.02 + 0.145 * { exp { -1 * {v + 26.5} / 10.0} }
            end
            v = v * 0.001 // reset v
            
            // Set correct units of tau
            tau = tau * 0.001

            //  inf
            float inf
            v = v * 1000 // v to units of equation
            inf =  1 / { 1 + {exp { -1*{v + 34.5} / 10}} } 
            v = v * 0.001 // reset v
            

            // alpha and beta
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            
            setfield NaF2 X_A->table[{i}] {alpha}
            setfield NaF2 X_B->table[{i}] {alpha + beta}
            v = v + dv

        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield NaF2 X_A->calc_mode 1 X_B->calc_mode 1
                    
        // Y table for gate h
        float dv = ({v_max} - {v_min})/{tab_divs}
        call NaF2 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 // 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 // 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 NaF2 Y_A->table[{i}] {alpha}
            setfield NaF2 Y_B->table[{i}] {alpha + beta}
            v = v + dv
        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield NaF2 Y_A->calc_mode 1 Y_B->calc_mode 1
end

//========================================================================
// P23RS   Tabchannel gNa-persistent (non-inactivating), gNa(P) 2005/03
//========================================================================
function make_NaP2
        str chanpath = "NaP2"
        if ({exists NaP2})
            return
        end
        create tabchannel NaP2
        setfield NaP2 \ 
            Ek              0.05 \
            Ik              0  \
            Xpower          1
        setfield NaP2 \
            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 NaP2 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 // 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
            // correct units of tau
            tau = tau * 0.001

            // inf
            float inf
            // A = 1, B = -10, Vhalf = -48, in units: Physiological Units
            // A = 1, B = -0.01, Vhalf = -0.048
            inf = 1 / ( {exp {(v + 0.048) / -0.01}} + 1)

            // alpha and beat
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            setfield NaP2 X_A->table[{i}] {alpha}
            setfield NaP2 X_B->table[{i}] {alpha + beta}
            v = v + dv
        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield NaP2 X_A->calc_mode 1 X_B->calc_mode 1
end

//========================================================================
//   P23RS    Tabchannel Anomalous Rectifier, gAR 2005/03
//========================================================================
function make_AR2
        if ({exists AR2})
            return
        end
        create tabchannel AR2
        setfield AR2 \ 
            Ek              -0.035 \
            Ik              0  \
            Xpower          1
        
        setfield AR2 \
            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 AR2 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 // 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
            
            // correct units of tau
            tau = tau * 0.001

            // inf
            float inf
                
            // A = 1, B = 5.5, Vhalf = -75, in units: Physiological Units
            // A = 1, B = 0.0055, Vhalf = -0.075
            inf = 1 / ( {exp {(v + 0.075) / 0.0055}} + 1)
        
            //  alpha and beta 
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            
            setfield AR2 X_A->table[{i}] {alpha}
            setfield AR2 X_B->table[{i}] {alpha + beta}
            v = v + dv
        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield AR2 X_A->calc_mode 1 X_B->calc_mode 1
end

//========================================================================
//  P23RS    Tabchannel gK-delayed rectifier, gK(DR) 2005/03
//========================================================================
function make_KDR2
        if ({exists KDR2})
            return
        end
        create tabchannel KDR2
        setfield KDR2 \ 
            Ek              -0.095 \
            Ik              0  \
            Xpower          4
        
        setfield KDR2 \
            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 KDR2 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 // 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
            tau = tau * 0.001 // correct units of tau

            //  inf
            float inf
            // A = 1, B = -10, Vhalf = -29.5, in units: Physiological Units
            // A = 1, B = -0.01, Vhalf = -0.0295
            inf = 1 / ( {exp {(v + 0.0295) / -0.01}} + 1)

            
            // alpha and beta 
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            setfield KDR2 X_A->table[{i}] {alpha}
            setfield KDR2 X_B->table[{i}] {alpha + beta}
            v = v + dv
        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield KDR2 X_A->calc_mode 1 X_B->calc_mode 1
end

//========================================================================
//   P23RS       Tabchannel gK-transient, gK(A) 2005/03
//========================================================================
function make_KA2
        if ({exists KA2})
            return
        end
        create tabchannel KA2
        setfield KA2 \ 
            Ek              -0.095 \
            Ik              0  \
            Xpower          4 \
            Ypower          1
        setfield KA2 \
            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 KA2 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 // 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
            // correct units of tau
            tau = tau * 0.001

            // inf
            float inf
                
            float A, B, Vhalf
                             

            // ChannelML form of equation: inf which is of form sigmoid, with params:
            // A = 1, B = -8.5, Vhalf = -60, in units: Physiological Units
            // A = 1, B = -0.0085, Vhalf = -0.06
            inf = 1 / ( {exp {(v + 0.06) /-0.0085}} + 1)
        
            // alpha and beta 
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            
            setfield KA2 X_A->table[{i}] {alpha}
            setfield KA2 X_B->table[{i}] {alpha + beta}
            v = v + dv
        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
        setfield KA2 X_A->calc_mode 1 X_B->calc_mode 1
                    
        // Y table for gate h
        float dv = ({v_max} - {v_min})/{tab_divs}
        call KA2 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 // 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
            // correct units of tau
            tau = tau * 0.001

            // inf
            float inf
                
            // A = 1, B = 6, Vhalf = -78, in units: Physiological Units
            // A = 1, B = 0.006, Vhalf = -0.078
            inf = 1 / ( {exp {(v + 0.078) / 0.006}} + 1)
        
            // alpha and beta
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            setfield KA2 Y_A->table[{i}] {alpha}
            setfield KA2 Y_B->table[{i}] {alpha + beta}
            v = v + dv
        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield KA2 Y_A->calc_mode 1 Y_B->calc_mode 1
end

//========================================================================
// P23RS          Tabchannel gK2-slow, gK2 2005/03
//========================================================================
function make_K22
        if ({exists K22})
            return
        end
        create tabchannel K22
        setfield K22 \ 
            Ek              -0.095 \
            Ik              0  \
            Xpower          1 \
            Ypower          1
        
        setfield K22 \
            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 K22 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 //  v to units of equat.
            tau = 4.95 + 0.5 / { {exp { {v - 81} / 25.6}} + {exp { {- v - 132} / 18 }}}
            v = v * 0.001 // reset v
            //  correct units of tau
            tau = tau * 0.001

            //  inf
            float inf
            // A = 1, B = -17, Vhalf = -10, in units: Physiological Units
            // A = 1, B = -0.017, Vhalf = -0.01
            inf = 1 / ( {exp {(v + 0.01) / -0.017}} + 1)

            // alpha and beta 
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            setfield K22 X_A->table[{i}] {alpha}
            setfield K22 X_B->table[{i}] {alpha + beta}
            v = v + dv
        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield K22 X_A->calc_mode 1 X_B->calc_mode 1
                    
        // Y table for gate h
        float dv = ({v_max} - {v_min})/{tab_divs}
        call K22 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 // 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
            // correct units of tau
            tau = tau * 0.001

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

            // alpha and beta
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            setfield K22 Y_A->table[{i}] {alpha}
            setfield K22 Y_B->table[{i}] {alpha + beta}
            v = v + dv
        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield K22 Y_A->calc_mode 1 Y_B->calc_mode 1
end

//========================================================================
// P23RS    Tabchannel gK-muscarinic receptor supressed, gK(M) 2005/03
//========================================================================
function make_KM2
        if ({exists KM2})
            return
        end
        create tabchannel KM2
        setfield KM2 \ 
            Ek              -0.095 \
            Ik              0  \
            Xpower          1
        setfield KM2 \
            Gbar 75 \
            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 KM2 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
            // A = 20, B = -0.005, Vhalf = -0.02
            alpha = 20 / ( {exp {(v + 0.02) / -0.005}} + 1)
        
            // beta
            float beta
            // A = 0.01, B = -18, Vhalf = -43, in units: Physiological Units
            // A = 10, B = -0.018, Vhalf = -0.043
            beta = 10 * {exp {(v + 0.043) / -0.018}}
        
            // alpha and beta 
            float tau = 1/(alpha + beta)
            setfield KM2 X_A->table[{i}] {alpha}
            setfield KM2 X_B->table[{i}] {alpha + beta}
            v = v + dv
        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
        setfield KM2 X_A->calc_mode 1 X_B->calc_mode 1
end

//========================================================================
//  P23RS   Tabchannel gCa(L)-low threshold, transient, gCa(L) 2005/03
//========================================================================
function make_CaL2
        if ({exists CaL2})
            return
        end
        create tabchannel CaL2
        setfield CaL2 \ 
            Ek              0.125 \
            Ik              0  \
            Xpower          2 \
            Ypower          1
        
        setfield CaL2 \
            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 CaL2 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 // 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
            // correct units of tau
            tau = tau * 0.001

            // inf
            float inf
                
            float A, B, Vhalf
            // A = 1, B = -6.2, Vhalf = -56.0, in units: Physiological Units
            // A = 1, B = -0.0062, Vhalf = -0.056
            inf = 1 / ( {exp {(v + 0.056) / -0.0062}} + 1)
        
            // alpha and beta
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            setfield CaL2 X_A->table[{i}] {alpha}
            setfield CaL2 X_B->table[{i}] {alpha + beta}
            v = v + dv
        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield CaL2 X_A->calc_mode 1 X_B->calc_mode 1
                    
        // Y table for gate h
        float dv = ({v_max} - {v_min})/{tab_divs}
        call CaL2 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 // 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
            // correct units of tau
            tau = tau * 0.001

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

            // alpha and beta
            float alpha
            float beta
            alpha = inf / tau   
            beta = (1- inf)/tau
            setfield CaL2 Y_A->table[{i}] {alpha}
            setfield CaL2 Y_B->table[{i}] {alpha + beta}
            v = v + dv
        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield CaL2 Y_A->calc_mode 1 Y_B->calc_mode 1
end

//==========================================================================
// P23RS    Tabchannel gCaH-high threshold calcium, gCa(L) "long" 2003/05
//==========================================================================
function make_CaH2
        if ({exists CaH2})
            return
        end
        create tabchannel CaH2
        setfield CaH2 \ 
            Ek              0.125 \
            Ik              0  \
            Xpower          2
        
        setfield CaH2 \
            Gbar 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 CaH2 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 units: Physiological Units
            // A = 1600, B = -0.013888889000000001, Vhalf = 0.005
            alpha = 1600 / ( {exp {(v - 0.005) / -0.013888889000000001}} + 1)
        
            //  beta
            float beta
                
            // A = 0.1, B = -5, Vhalf = -8.9, in units: Physiological Units
            // A = 100, B = -0.005, Vhalf = -0.0089
            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

            //  alpha and beta 
            float tau = 1/(alpha + beta)
            setfield CaH2 X_A->table[{i}] {alpha}
            setfield CaH2 X_B->table[{i}] {alpha + beta}
            v = v + dv
        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield CaH2 X_A->calc_mode 1 X_B->calc_mode 1
end

//========================================================================
//   P23RS   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_s2
        if ({exists Ca_s2})
            return
        end
        create Ca_concen Ca_s2
        // params for soma Ca pool 
        setfield Ca_s2 \
            tau                   { 1.0 / 10 }    \
            Ca_base               0
        addfield Ca_s2 addmsg1
        setfield Ca_s2 \
                addmsg1        "../CaH2 . I_Ca Ik"
//        addfield Ca_s2 addmsg2
//        setfield Ca_s2 \
//                addmsg2        "../CaL2 . 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_d2
        if ({exists Ca_d2})
            return
        end
        create Ca_concen Ca_d2
        // params for dend. Ca pool model
        setfield Ca_d2 \
            tau                   { 1.0 / 50 }    \
            Ca_base               0

        addfield Ca_d2 addmsg1
        setfield Ca_d2 \
                addmsg1        "../CaH2 . I_Ca Ik"
//        addfield Ca_d2 addmsg2
//        setfield Ca_d2 \
//                addmsg2        "../CaL2 . 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.
*/

//===============================================================================
//  P23RS Ca-dependent K Channel K(C)
//===============================================================================
/*
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_KCs2
        if ({exists KCs2})
            return
        end
        create tabchannel KCs2
        setfield KCs2 \ 
            Ek              -0.095 \
            Ik              0  \
            Xpower          1 \
            Zpower          1
        setfield KCs2 \
            Gbar 120 \
            Gk              0 
        float tab_divs = 1041
        float v_min = -0.12
        float v_max = 0.14
        float v, dv, i
            
        // X table for gate m
        float dv = ({v_max} - {v_min})/{tab_divs}
        call KCs2 TABCREATE X {tab_divs} {v_min} {v_max}
        v = {v_min}
        for (i = 0; i <= ({tab_divs}); i = i + 1)
            
            // alpha
            float alpha
            v = v * 1000 // 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
            //  correct units of alpha
            alpha = alpha * 1000

            
            // beta
            float beta
            v = v * 1000 // v to units of equation
            alpha = alpha * 0.001 // alpha to units of equation
            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
            // correct units of beta
            beta = beta * 1000

            // alpha and beta
            float tau = 1/(alpha + beta)
            
            setfield KCs2 X_A->table[{i}] {alpha}
            setfield KCs2 X_B->table[{i}] {alpha + beta}
            v = v + dv
        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield KCs2 X_A->calc_mode 1 X_B->calc_mode 1
                    
        // Ca dependent term (voltage independent)
        float conc_min = 0
        float conc_max = 1000
        float dc = ({conc_max} - {conc_min})/{tab_divs}
        float ca_conc = {conc_min}
        call KCs2 TABCREATE  Z {tab_divs} {conc_min} {conc_max}
        float const_state
        for (i = 0; i <= ({tab_divs}); i = i + 1)
            ca_conc = ca_conc * 0.000001 // ca_conc to units of equation
            if (ca_conc < 0.00025 )
                const_state =  {ca_conc / 0.00025} 
            else
                const_state =  1
            end
            ca_conc = ca_conc * 1000000 //reset  ca_conc
            
            setfield KCs2 Z_A->table[{i}] {0}
            setfield KCs2 Z_B->table[{i}] {const_state}
            ca_conc= ca_conc + dc
        end
        tweaktau KCs2 Z
        
        addfield KCs2 addmsg1
        setfield KCs2 addmsg1  "../Ca_s2  . CONCEN Ca"
end


function make_KCd2
        if ({exists KCd2})
            return
        end
        create tabchannel KCd2
        setfield KCd2 \ 
            Ek              -0.095 \
            Ik              0  \
            Xpower          1 \
            Zpower          1
        setfield KCd2 \
            Gbar 120 \
            Gk              0 
        float tab_divs = 1041
        float v_min = -0.12
        float v_max = 0.14
        float v, dv, i
            
        // X table for gate m
        float dv = ({v_max} - {v_min})/{tab_divs}
        call KCd2 TABCREATE X {tab_divs} {v_min} {v_max}
        v = {v_min}
        for (i = 0; i <= ({tab_divs}); i = i + 1)

            //  alpha
            float alpha
            v = v * 1000 // 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
            // correct units of alpha
            alpha = alpha * 1000

            // beta
            float beta
            v = v * 1000 // v to units of equation
            alpha = alpha * 0.001 // alpha to units of equation
            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
                        
            // correct units of beta
            beta = beta * 1000
            
            //alpha and beta 
            float tau = 1/(alpha + beta)
            
            setfield KCd2 X_A->table[{i}] {alpha}
            setfield KCd2 X_B->table[{i}] {alpha + beta}
            v = v + dv
        end // end of for (i = 0; i <= ({tab_divs}); i = i + 1)
            
        setfield KCd2 X_A->calc_mode 1 X_B->calc_mode 1
                    
        // Ca dependent term (voltage independent)
        float conc_min = 0
        float conc_max = 1000
        float dc = ({conc_max} - {conc_min})/{tab_divs}
        float ca_conc = {conc_min}
        call KCd2 TABCREATE  Z {tab_divs} {conc_min} {conc_max}
        float const_state
        for (i = 0; i <= ({tab_divs}); i = i + 1)
            ca_conc = ca_conc * 0.000001 // ca_conc to units of equation
            if (ca_conc < 0.00025 )
                const_state =  {ca_conc / 0.00025} 
            else
                const_state =  1
            end
            ca_conc = ca_conc * 1000000 //reset ca_conc 
            
            setfield KCd2 Z_A->table[{i}] {0}
            setfield KCd2 Z_B->table[{i}] {const_state}
            ca_conc= ca_conc + dc
        end
        tweaktau KCd2 Z
        
        addfield KCd2 addmsg1
        setfield KCd2 addmsg1  "../Ca_d2  . CONCEN Ca"
end


//========================================================================
//              P23RS  Ca-dependent K AHP Channel,gK(AHP) 
//========================================================================

/* This is a tabchannel which gets the calcium concentration from Ca pool
   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_KAHPs2
        if ({exists KAHPs2})
            return
        end
        create tabchannel KAHPs2
        setfield KAHPs2 \ 
            Ek              -0.095 \
            Ik              0  \
            Zpower          1
        
        setfield KAHPs2 \
            Gbar 1 \
            Gk              0 
        float tab_divs = 1041
        // Ca dependent channel 
        float c
        float conc_min = 0
        float conc_max = 1000
        float dc = ({conc_max} - {conc_min})/{tab_divs}
        float ca_conc = {conc_min}
        call KAHPs2 TABCREATE Z {tab_divs} {conc_min} {conc_max}
        for (c = 0; c <= ({tab_divs}); c = c + 1)
                    
            // alpha
            float alpha
            float v
            ca_conc = ca_conc * 0.000001 // ca_conc to units of equation
            if (ca_conc < 0.0001 )
                alpha =  ca_conc/0.01 
            else
                alpha =  0.01
            end
            ca_conc = ca_conc * 1000000 // resetting ca_conc 
            // correct units of alpha
            alpha = alpha * 1000

            // beta
            float beta
            ca_conc = ca_conc * 0.000001 // ca_conc to units of equation
            beta = 0.01
            ca_conc = ca_conc * 1000000 // resetting ca_conc 
            // correct units of beta
            beta = beta * 1000

            // alpha and beta 

            float tau = 1/(alpha + beta)
            setfield KAHPs2 Z_A->table[{c}] {alpha}
            setfield KAHPs2 Z_B->table[{c}] {alpha + beta}
                    ca_conc = ca_conc + dc
        end // end of for (c = 0; c <= ({tab_divs}); c = c + 1)
                
        setfield KAHPs2 Z_conc 1
        setfield KAHPs2 Z_A->calc_mode 1 Z_B->calc_mode 1

        addfield KAHPs2 addmsg1
        setfield KAHPs2  \
                addmsg1        "../Ca_s2 . CONCEN Ca"
end


function make_KAHPd2
        if ({exists KAHPd2})
            return
        end
        create tabchannel KAHPd2
        setfield KAHPd2 \ 
            Ek              -0.095 \
            Ik              0  \
            Zpower          1
        setfield KAHPd2 \
            Gbar 1 \
            Gk              0 
        float tab_divs = 1041

        float c
        float conc_min = 0
        float conc_max = 1000
        float dc = ({conc_max} - {conc_min})/{tab_divs}
        float ca_conc = {conc_min}
        call KAHPd2 TABCREATE Z {tab_divs} {conc_min} {conc_max}
        for (c = 0; c <= ({tab_divs}); c = c + 1)
                    
            // alpha
            float alpha
            ca_conc = ca_conc * 0.000001 // ca_conc to units of equation
            if (ca_conc < 0.0001 )
                alpha =  ca_conc/0.01 
            else
                alpha =  0.01
            end
            ca_conc = ca_conc * 1000000 // reset ca_conc 
            // correct units of alpha
            alpha = alpha * 1000

            // beta
            float beta
            ca_conc = ca_conc * 0.000001 // ca_conc to units of equation
            beta = 0.01
            ca_conc = ca_conc * 1000000 // reset ca_conc 
            // correct units of beta
            beta = beta * 1000

            // alpha and beta
            float tau = 1/(alpha + beta)
            
            setfield KAHPd2 Z_A->table[{c}] {alpha}
            setfield KAHPd2 Z_B->table[{c}] {alpha + beta}
                    ca_conc = ca_conc + dc
        end // end of for (c = 0; c <= ({tab_divs}); c = c + 1)
                
        setfield KAHPd2 Z_conc 1
        setfield KAHPd2 Z_A->calc_mode 1 Z_B->calc_mode 1

        addfield KAHPd2 addmsg1
        setfield KAHPd2  \
                addmsg1        "../Ca_d2 . CONCEN Ca"
end


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