Auditory cortex layer IV network model (Beeman 2013)

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Accession:150678
"... The primary objective of this modeling study was to determine the effects of axonal conduction velocity (often neglected, but significant), as well as synaptic time constants, on the ability of such a network to create and propagate cortical waves. ... The model is also being used to study the interaction between single and two-tone input and normal background activity, and the effects of synaptic depression from thalamic inputs. The simulation scripts have the additional purpose of serving as tutorial examples for the construction of cortical networks with GENESIS. The present model has fostered the development of the G-3 Python network analysis and visualization tools used in this study... It is my hope that this short tutorial and the example simulation scripts can provide a head start for a graduate student or postdoc who is beginning a cortical modeling project. "
Reference:
1 . Beeman D (2013) A modeling study of cortical waves in primary auditory cortex BMC Neuroscience 14(Supl 1):P23
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism: Auditory cortex;
Cell Type(s): Neocortex V1 pyramidal corticothalamic cell; Neocortex V1 basket intratelencephalic cell;
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: GENESIS;
Model Concept(s): Activity Patterns; Tutorial/Teaching;
Implementer(s): Beeman, Dave;
Search NeuronDB for information about:  Neocortex V1 pyramidal corticothalamic cell; Neocortex V1 basket intratelencephalic cell;
  
// genesis - pyrchans.g - channels for cortical pyramidal cells
// based on genesis/Scripts/neurokit/prototypes/traub91chan.g 

/* Note some hacks below:
   I've added an optional chanpath arg to the make_xxx_traub91 functions
   to allow renaming them.  But, if the Ca-dependent channels are to
   work properly, the Ca_concen element must be named "Ca_conc" and
   the Ca channel must be named Ca_hip_traub91
*/

/* 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.
*/

// CONSTANTS
float EREST_ACT = -0.060 /* hippocampal cell resting potl */
float ENA = 0.115 + EREST_ACT // 0.055
float EK = -0.015 + EREST_ACT // -0.075
float ECA = 0.140 + EREST_ACT // 0.080
float SOMA_A = 3.320e-9       // soma area m^2 - usually will be changed

/*
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.
*/

//========================================================================
//                      Tabulated Ca Channel
//========================================================================

function make_Ca_hip_traub91
   str chanpath = "Ca_hip_traub91"
    if ({argc} == 1)
       chanpath = {argv 1}
    end
    if ({exists {chanpath}})
       return
    end
    create tabchannel {chanpath}
                setfield        ^       \
                Ek              {ECA}   \               //      V
                Gbar            { 40 * SOMA_A }      \  //      S
                Ik              0       \               //      A
                Gk              0       \               //      S
                Xpower  2       \
                Ypower  1       \
                Zpower  0

/*
Often, the alpha and beta rate parameters can be expressed in the functional
form y = (A + B * x) / (C + {exp({(x + D) / F})}).  When this is the case,
case, the command "setupalpha chan gate AA AB AC AD AF BA BB BC BD BF" can be
used to simplify the process of initializing the A and B tables for the X, Y
and Z gates.  Although setupalpha has been implemented as a compiled GENESIS
command, it is also defined as a script function in the neurokit/prototypes
defaults.g file.  Although this command can be used as a "black box", its
definition shows some nice features of the tabchannel object, and some tricks
we will need when the rate parameters do not fit this form.
*/

// Converting Traub's expressions for the gCa/s alpha and beta functions
// to SI units and entering the A, B, C, D and F parameters, we get:

        setupalpha {chanpath} X 1.6e3  \
                 0 1.0 {-1.0 * (0.065 + EREST_ACT) } -0.01389       \
                 {-20e3 * (0.0511 + EREST_ACT) }  \
                 20e3 -1.0 {-1.0 * (0.0511 + EREST_ACT) } 5.0e-3
/* 
   The Y gate (gCa/r) is not quite of this form.  For V > EREST_ACT, alpha =
   5*{exp({-50*(V - EREST_ACT)})}.  Otherwise, alpha = 5.  Over the entire
   range, alpha + beta = 5.  To create the Y_A and Y_B tables, we use some
   of the pieces of the setupalpha function.
*/

// Allocate space in the A and B tables with room for xdivs+1 = 50 entries,
// covering the range xmin = -0.1 to xmax = 0.05.
        float   xmin = -0.1
        float   xmax = 0.05
        int     xdivs = 49
	call {chanpath} TABCREATE Y {xdivs} {xmin} {xmax}

// Fill the Y_A table with alpha values and the Y_B table with (alpha+beta)
        int i
        float x,dx,y
        dx = (xmax - xmin)/xdivs
        x = xmin
        for (i = 0 ; i <= {xdivs} ; i = i + 1)
	    if (x > EREST_ACT)
                y = 5.0*{exp {-50*(x - EREST_ACT)}}
	    else
		y = 5.0
	    end
            setfield {chanpath} Y_A->table[{i}] {y}
            setfield {chanpath} Y_B->table[{i}] 5.0
            x = x + dx
        end

// For speed during execution, set the calculation mode to "no interpolation"
// and use TABFILL to expand the table to 3000 entries.
           setfield {chanpath} Y_A->calc_mode 0   Y_B->calc_mode 0
           call {chanpath} TABFILL Y 3000 0
end

/****************************************************************************
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.  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 be typically be determined by the cell reader from the cell
parameter file.  However, for the prototype channel we wlll 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.

****************************************************************************/

//========================================================================
//                      Ca conc
//========================================================================

/* This one has to be named Ca_conc, however */

function make_Ca_hip_conc
    str chanpath = "Ca_conc"
    if ({argc} == 1)
       chanpath = {argv 1}
    end
    if ({exists {chanpath}})
       return
    end
        create Ca_concen Ca_conc
        setfield Ca_conc \
                tau     0.01333   \      // sec
                B       17.402e12 \      // Curr to conc for soma
                Ca_base 0.0
        addfield Ca_conc addmsg1
        setfield Ca_conc \
                addmsg1        "../Ca_hip_traub91 . 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 most 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.
*/

//========================================================================
//             Tabulated Ca-dependent K AHP Channel
//========================================================================

/* 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_Kahp_hip_traub91
    str chanpath = "Kahp_hip_traub91"
    if ({argc} == 1)
       chanpath = {argv 1}
    end
    if ({exists {chanpath}})
       return
    end
        create  tabchannel      {chanpath}
                setfield        ^       \
                Ek              {EK}   \               //      V
                Gbar            { 8 * SOMA_A }    \    //      S
                Ik              0       \              //      A
                Gk              0       \              //      S
                Xpower  0       \
                Ypower  0       \
                Zpower  1

// Allocate space in the Z gate A and B tables, covering a concentration
// range from xmin = 0 to xmax = 1000, with 50 divisions
        float   xmin = 0.0
        float   xmax = 1000.0
        int     xdivs = 50

        call {chanpath} TABCREATE Z {xdivs} {xmin} {xmax}
        int i
        float x,dx,y
        dx = (xmax - xmin)/xdivs
        x = xmin
        for (i = 0 ; i <= {xdivs} ; i = i + 1)
            if (x < 500.0)
                y = 0.02*x
            else
                y = 10.0
            end
            setfield {chanpath} Z_A->table[{i}] {y}
            setfield {chanpath} Z_B->table[{i}] {y + 1.0}
            x = x + dx
        end
// For speed during execution, set the calculation mode to "no interpolation"
// and use TABFILL to expand the table to 3000 entries.
        setfield {chanpath} Z_A->calc_mode 0   Z_B->calc_mode 0
        call {chanpath} TABFILL Z 3000 0
// Use an added field to tell the cell reader to set up the
// CONCEN message from the Ca_hip_concen element
        addfield {chanpath} addmsg1
        setfield {chanpath} \
                addmsg1        "../Ca_conc . CONCEN Ca"
end

//========================================================================
//  Voltage- and 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_Kc_hip_traub91
    str chanpath = "Kc_hip_traub91"
    if ({argc} == 1)
       chanpath = {argv 1}
    end
    if ({exists {chanpath}})
       return
    end
    create  tabchannel      {chanpath}
                setfield        ^       \
                Ek              {EK}    \                       //      V
                Gbar            { 100.0 * SOMA_A }      \       //      S
                Ik              0       \                       //      A
                Gk              0                               //      S

// Now make a X-table for the voltage-dependent activation parameter.
        float   xmin = -0.1
        float   xmax = 0.05
        int     xdivs = 49
        call {chanpath} TABCREATE X {xdivs} {xmin} {xmax}
        int i
        float x,dx,alpha,beta
        dx = (xmax - xmin)/xdivs
        x = xmin
        for (i = 0 ; i <= {xdivs} ; i = i + 1)
            if (x < EREST_ACT + 0.05)
                alpha = {exp {53.872*(x - EREST_ACT) - 0.66835}}/0.018975
                    beta = 2000*{exp {(EREST_ACT + 0.0065 - x)/0.027}} - alpha
            else
                alpha = 2000*{exp {(EREST_ACT + 0.0065 - x)/0.027}}
                beta = 0.0
            end
            setfield {chanpath} X_A->table[{i}] {alpha}
            setfield {chanpath} X_B->table[{i}] {alpha+beta}
            x = x + dx
        end

// Expand the tables to 3000 entries to use without interpolation
    setfield {chanpath} X_A->calc_mode 0 X_B->calc_mode 0
    setfield {chanpath} Xpower 1
    call {chanpath} TABFILL X 3000 0

// Create a table for the function of concentration, allowing a
// concentration range of 0 to 1000, with 50 divisions.  This is done
// using the Z gate, which can receive a CONCEN message.  By using
// the "instant" flag, the A and B tables are evaluated as lookup tables,
//  rather than being used in a differential equation.
        float   xmin = 0.0
        float   xmax = 1000.0
        int     xdivs = 50

        call {chanpath} TABCREATE Z {xdivs} {xmin} {xmax}
        int i
        float x,dx,y
        dx = (xmax - xmin)/xdivs
        x = xmin
        for (i = 0 ; i <= {xdivs} ; i = i + 1)
            if (x < 250.0)
                y = x/250.0
            else
                y = 1.0
            end
            /* activation will be computed as Z_A/Z_B */
            setfield {chanpath} Z_A->table[{i}] {y}
            setfield {chanpath} Z_B->table[{i}] 1.0
            x = x + dx
        end
        setfield {chanpath} Z_A->calc_mode 0 Z_B->calc_mode 0
        setfield {chanpath} Zpower 1
// Make it an instantaneous gate (no time constant)
    setfield {chanpath} instant {INSTANTZ}
// Expand the table to 3000 entries to use without interpolation.
    call {chanpath} TABFILL Z 3000 0

// Now we need to provide for messages that link to external elements.
// The message that sends the Ca concentration to the Z gate tables is stored
// in an added field of the channel, so that it may be found by the cell
// reader.
        addfield Kc_hip_traub91 addmsg1
        setfield Kc_hip_traub91 addmsg1  "../Ca_conc  . CONCEN Ca"
end

// The remaining channels are straightforward tabchannel implementations

//========================================================================
//                Tabchannel Na Hippocampal cell channel
//========================================================================
function make_Na_hip_traub91

    str chanpath = "Na_hip_traub91"
    if ({argc} == 1)
       chanpath = {argv 1}
    end
    if ({exists {chanpath}})
       return
    end
        create  tabchannel      {chanpath}
                setfield        ^       \
                Ek              {ENA}   \               //      V
                Gbar            { 300 * SOMA_A }    \   //      S
                Ik              0       \               //      A
                Gk              0       \               //      S
                Xpower  2       \
                Ypower  1       \
                Zpower  0

        setupalpha {chanpath} X {320e3 * (0.0131 + EREST_ACT)}  \
                 -320e3 -1.0 {-1.0 * (0.0131 + EREST_ACT) } -0.004       \
                 {-280e3 * (0.0401 + EREST_ACT) } \
                 280e3 -1.0 {-1.0 * (0.0401 + EREST_ACT) } 5.0e-3

        setupalpha {chanpath} Y 128.0 0.0 0.0  \
                {-1.0 * (0.017 + EREST_ACT)} 0.018  \
                4.0e3 0.0 1.0 {-1.0 * (0.040 + EREST_ACT) } -5.0e-3
end

//========================================================================
//                Tabchannel K(DR) Hippocampal cell channel
//========================================================================
function make_Kdr_hip_traub91
    str chanpath = "Kdr_hip_traub91"
    if ({argc} == 1)
       chanpath = {argv 1}
    end
    if ({exists {chanpath}})
       return
    end
        create  tabchannel      {chanpath}
                setfield        ^       \
                Ek              {EK}	\	           //      V
                Gbar            { 150 * SOMA_A }    \      //      S
                Ik              0       \                  //      A
                Gk              0       \                  //      S
                Xpower  1       \
                Ypower  0       \
                Zpower  0

                setupalpha {chanpath} X               \
                           {16e3 * (0.0351 + EREST_ACT)}   \  // AA
                           -16e3                           \  // AB
                           -1.0                            \  // AC
                           {-1.0 * (0.0351 + EREST_ACT) }  \  // AD
                           -0.005                          \  // AF
                           250                             \  // BA
                           0.0                             \  // BB
                           0.0                             \  // BC
                           {-1.0 * (0.02 + EREST_ACT)}     \  // BD
                           0.04                               // BF
end

//========================================================================
//                Tabchannel K(A) Hippocampal cell channel
//========================================================================
function make_Ka_hip_traub91
    str chanpath = "Ka_hip_traub91"
    if ({argc} == 1)
       chanpath = {argv 1}
    end
    if ({exists {chanpath}})
       return
    end
        create  tabchannel      {chanpath}
                setfield        ^       \
                Ek              {EK}    \	          //      V
                Gbar            { 50 * SOMA_A }     \     //      S
                Ik              0       \                 //      A
                Gk              0       \                 //      S
                Xpower  1       \
                Ypower  1       \
                Zpower  0

        setupalpha {chanpath} X {20e3 * (0.0131 + EREST_ACT)}  \
                 -20e3 -1.0 {-1.0 * (0.0131 + EREST_ACT) } -0.01    \
                 {-17.5e3 * (0.0401 + EREST_ACT) }  \
                 17.5e3 -1.0 {-1.0 * (0.0401 + EREST_ACT) } 0.01

        setupalpha {chanpath} Y 1.6 0.0 0.0  \
                {0.013 - EREST_ACT} 0.018  \
                50.0 0.0 1.0 {-1.0 * (0.0101 + EREST_ACT) } -0.005
end


//========================================================================
//                Synaptically activated channels
//========================================================================

float EAMPA = 0.0
float EGABA = -0.080

function make_AMPA_pyr
    str chanpath = "AMPA_pyr"
    if ({argc} == 1)
       chanpath = {argv 1}
    end
    if ({exists {chanpath}})
       return
    end
    float tau1 = 0.003
    float tau2 = 0.003
    create  synchan      {chanpath}
    setfield        ^       \
        Ek                      {EAMPA} \
        tau1            {tau1} \        // sec
        tau2            {tau2} \        // sec
        gmax            0 // Siemens
end


function make_GABA_pyr
    str chanpath = "GABA_pyr"
    if ({argc} == 1)
       chanpath = {argv 1}
    end
    if ({exists {chanpath}})
       return
    end
    float tau1 = 0.003
    float tau2 = 0.008
    create  synchan      {chanpath}
    setfield        ^       \
        Ek                      {EGABA} \
        tau1            {tau1} \        // sec
        tau2            {tau2} \        // sec
        gmax            0 // Siemens
end


Beeman D (2013) A modeling study of cortical waves in primary auditory cortex BMC Neuroscience 14(Supl 1):P23

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References and models that cite this paper

Cornelis H, Coop AD, Bower JM (2012) A federated design for a neurobiological simulation engine: the CBI federated software architecture. PLoS One 7:e28956 [PubMed]

Rodriguez AL, Cornelis H, Beeman D, Bower JM (2012) Multiscale modeling with GENESIS 3, using the G-shell and Python BMC Neuroscience 13(Supl 1):P176

(2 refs)