File contents
//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.
*/
// 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 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.
*/
//========================================================================
// Tabulated Ca Channel
//========================================================================
function make_Ca
if ({exists Ca})
return
end
create tabchannel Ca
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 Ca 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 Ca 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 Ca Y_A->table[{i}] {y}
setfield Ca 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 Ca Y_A->calc_mode 0 Y_B->calc_mode 0
call Ca 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
//========================================================================
function make_Ca_conc
if ({exists Ca_conc})
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 . 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" refers to the sibling element Ca and "."
refers to the Ca_conc element itself.
*/
//========================================================================
// Tabulated Ca-dependent K AHP Channel
//========================================================================
/* This is a tabchannel which gets the calcium concentration from Ca_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_K_AHP
if ({exists K_AHP})
return
end
create tabchannel K_AHP
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 K_AHP 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 K_AHP Z_A->table[{i}] {y}
setfield K_AHP 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 K_AHP Z_A->calc_mode 0 Z_B->calc_mode 0
call K_AHP TABFILL Z 3000 0
// Use an added field to tell the cell reader to set up the
// CONCEN message from the Ca_concen element
addfield K_AHP addmsg1
setfield K_AHP \
addmsg1 "../Ca_conc . CONCEN Ca"
end
//========================================================================
// Ca-dependent K Channel - K(C) - (vdep_channel with table and tabgate)
//========================================================================
/*
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_K_C
if ({exists K_C})
return
end
create tabchannel K_C
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 K_C 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 K_C X_A->table[{i}] {alpha}
setfield K_C X_B->table[{i}] {alpha+beta}
x = x + dx
end
// Expand the tables to 3000 entries to use without interpolation
setfield K_C X_A->calc_mode 0 X_B->calc_mode 0
setfield K_C Xpower 1
call K_C 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 K_C 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 K_C Z_A->table[{i}] {y}
setfield K_C Z_B->table[{i}] 1.0
x = x + dx
end
setfield K_C Z_A->calc_mode 0 Z_B->calc_mode 0
setfield K_C Zpower 1
// Make it an instantaneous gate (no time constant)
setfield K_C instant {INSTANTZ}
// Expand the table to 3000 entries to use without interpolation.
call K_C 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 K_C addmsg1
setfield K_C addmsg1 "../Ca_conc . CONCEN Ca"
end
// The remaining channels are straightforward tabchannel implementations
//========================================================================
// Tabchannel Na Hippocampal cell channel
//========================================================================
function make_Na
if ({exists Na})
return
end
create tabchannel Na
setfield ^ \
Ek {ENA} \ // V
Gbar { 300 * SOMA_A } \ // S
Ik 0 \ // A
Gk 0 \ // S
Xpower 2 \
Ypower 1 \
Zpower 0
setupalpha Na 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 Na 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_K_DR
if ({exists K_DR})
return
end
create tabchannel K_DR
setfield ^ \
Ek {EK} \ // V
Gbar { 150 * SOMA_A } \ // S
Ik 0 \ // A
Gk 0 \ // S
Xpower 1 \
Ypower 0 \
Zpower 0
setupalpha K_DR 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_K_A
if ({exists K_A})
return
end
create tabchannel K_A
setfield ^ \
Ek {EK} \ // V
Gbar { 50 * SOMA_A } \ // S
Ik 0 \ // A
Gk 0 \ // S
Xpower 1 \
Ypower 1 \
Zpower 0
setupalpha K_A 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 K_A 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
Click here to get the file
ebook "Neural Networks as Cybernetic Systems" (3rd edition)