File contents
Object Type: tabchannel
Description: Hodgkin-Huxley type voltage activated channel with tabulated
equations.
Author: E. De Schutter, Caltech (1/91)
------------------------------------------------------------------------------
ELEMENT PARAMETERS
DataStructure: tab_channel_type [in src/olf/olf_struct.h]
Size: 168 bytes
Fields:
activation channel activation
Gk channel conductance
Ik channel current
Ek channel reversal potential
Gbar channel maximum conductance
X value of X gate; optional gate, X=m
Y value of Y gate; optional gate, X=h
Z value of Z gate; optional gate, Z is
concentration-dependent
X_A table for alpha function for X
X_B table for beta function for X
X_alloced flag for allocation of X_A and X_B
Y_A table for alpha function for Y
Y_B table for beta function for Y
Y_alloced flag for allocation of Y_A and Y_B
Z_A table for alpha function for Z
Z_B table for beta function for Z
Z_alloced flag for allocation of Z_A and Z_B
Xpower power to raise X gate to
Ypower power to raise Y gate to
Zpower power to raise Z gate to
instant {INSTANTX}, {INSTANTY}, or {INSTANTZ} to
determine the gate to instantly set to A/B
surface compartment surface area used with DOMAINCONC
------------------------------------------------------------------------------
SIMULATION PARAMETERS
Function: TabChannel [in src/olf/tabchannel.c]
Classes: segment channel
Actions: CALC_BETA CALC_ALPHA CALC_MINF DUMP RESTORE2 SAVE2
SHOW SET TABDELETE TABFILL TABCREATE TABREAD TABSAVE
CHECK PROCESS RESET INIT
Messages: VOLTAGE voltage [membrane voltage of compartment]
EK Ek [reversal potential]
CONCEN concen [ion concentration sent to channel]
DOMAINCONC Ik scale [ion current from another channel, to
be multiplied by scale, and divided by
surface field]
ADD_GBAR offset [increment to be added to Gbar]
------------------------------------------------------------------------------
Notes: Tabulated hh-like channel. The standard voltage dependent
activation (X) and inactivation (Y) factors are present. For
concentration dependent processes a third factor (Z) has
added. Z can do a lot of things; the most important is that
it gets a different message (CONCEN) than X and Y (VOLTAGE).
Standard use for Z is concentration dependent inactivation,
using a Zpower > 0. An alternative is to use it for
codependent activation; using Zpower<0, Z will equal concen
value times v-dependent table-value. The DOMAINCONC message
provides a highly simplified model to obtain the ionic
concentration directly, using the current sent from another
channel, times a scale factor, and dividing by the surface
area of the parent compartment.
The table for the object is created using a call to the
TABCREATE action of the object. For computational efficiency
the forward rate factor alpha (A) and 1/tau (B) are tabulated
in A-table and B-table.
The tabchannel element is very similar to the hh_channel
element, except that it uses tables for the voltage and other
dependencies. It speeds up computation by using table lookups
rather than calculations depending on exponentials. It also
provides more flexibility, being able to specify voltage
dependencies not falling in the traditional Hodgkin-Huxley
forms.
The gate obeys the following equations:
dX/dt = A_X - B_X*X
dY/dt = A_Y - B_Y*Y
dZ/dt = A_Z - B_Z*Z
Gk = Gbar X^Xpower} Y^Ypower} Z^Zpower}
Ik = Gk * (Ek - V)
NOTE: These equations are slightly different from the usual
Hodgkin-Huxley equations where:
dX/dt = alpha*(1 - X) - beta*X
The tables in this element are therefore actually A = alpha,
and B = 1/tau = alpha + beta. This change reduces the number
of calculations to be made on the table output during the
integration.
The alpha and beta functions of the X, Y and Z gates are
implemented as tables and therefore have to be explicitly
allocated using the TABCREATE function. Copies of tabchannel
use the original arrays unless new arrays are explicitly
allocated. The X and Y gates use the same VOLTAGE message.
The Z gate uses the CONCEN message, which can be any field. It
allows for dependencies on other parameters.
The instant field may be set to {INSTANTX}, {INSTANTY}, or
{INSTANTZ} to specify that the X, Y, or Z gate value will
be instantly set to A/B, rather than using the A and B
table values in the differential equations above. This
allows the channel conductance to have a multiplicative
factor of A/B. This is often used with the Z gate to model
a Ca-dependent conductance, or to implement Morris-Lecar
models having zero time constant for activation. For an
example, see the implementation of the Ca-dependent K
Channel in Scripts/neurokit/prototypes/traub91chan.g.
The TABCREATE function
TABCREATE here is different from the table and tabgate
elements. We only need to specify which gate to set up, and
both tables for the gate will be filled.
call <element> TABCREATE <X/Y/Z> <xdivs> <xmin> <xmax>
This call creates two tables for X, Y, or Z with indices from
0 to xdivs, i.e. xdvivs + 1 entries which span the range xmin
to xmax. Values outside this range are linearly extrapolated
using the nearest 2 table entries.
Entries in these tables are made with statements like
setfield Na_chan X_A->table[0] 0.05
There are several alternatives to using a long sequence of
setfield commands to fill the tables. The file2tab command
can be used to fill the tables from a file of values. If the
rate (alpha and beta) or state (tau and minf) variables can be
expressed as a mathematical function, a for loop may be used
to fill the tables. For functions of the form (A + B * x) /
(C + exp((x + D) / F)), the setupalpha or setuptau commands
may be used. This is also discussed in Chapter 19 of The
Book of GENESIS (2nd ed.)
The TABDELETE function
When deleting tabchannels, or the cells or compartments
containing them, you must call TABDELETE first, in order to
deallocate the memory for the tables. Finally, you have to
give the "reclaim" command for the memory to actually be
freed. Note that the tables are shared among all tabchannels
that are created by copy or readcell from a prototype.
Therefore, you shouldn't call TABDELETE unless you plan to
delete all copies of the tabchannel.
The TABFILL function
TABFILL expands the table by using interpolation on the
existing table entries. Again, the syntax is different from
that for table and tabgate elements, and one just has to call
TABFILL once to fill both the arrays corresponding to that
gate:
call <element> TABFILL <X/Y/Z> <xdivs> <fill_mode>
xdivs specifies the number of divisions that the expanded
tables should have.
fill_mode is one of
0 = B-spline fill (default)
1 = cubic spline fill (not yet implemented)
2 = Linear fill
Tables have a calc_mode field that is by default set to
LIN_INTERP (a pre-defined global variable equal to one), so
that linear interpolation is performed at run time, allowing
the use of a smaller table. If sufficient memory is
available, it will be faster to perform the interpolation when
the table is created, by expanding it with TABFILL. Then, run
time interpolation should be disabled by setting the calc_mode
of the tables to NO_INTERP (zero). For example:
setfield {chanpath} X_A->calc_mode {NO_INTERP}
setfield {chanpath} X_B->calc_mode {NO_INTERP}
The TABSAVE and TABREAD functions
As filling the tables can be time-consuming (particularly if
it is done using a for loop in a script), the TABSAVE and
TABREAD functions can be useful for saving channel tables and
re-loading them when the simulation is run again.
TABSAVE may be called after the channel has been created and
set up, in order wto save the tables to a file. For example:
call Purk_Kdr TABSAVE Purk_Kdr.tab
TABREAD is called after the channel has been created and the
tables have been allocated. For example:
if (!{exists Purk_Kdr})
create tabchannel Purk_Kdr
setfield Purk_Kdr Ek {EK} Gbar {GK} Ik 0 Gk 0 \
Xpower 2 Ypower 1 Zpower 0
call Purk_Kdr TABCREATE X {xdivs} {xmin} {xmax}
call Purk_Kdr TABCREATE Y {xdivs} {xmin} {xmax}
end
call Purk_Kdr TABREAD Purk_Kdr.tab
Scaling tables
When the fields X_A->sx, X_A->sy, X_A->ox, X_A->oy, and the
corresponding fields on X_B, Y_A, Y_B, Z_A, Z_B are set, the
tabgate element automatically scales on the entries in the
interpol_struct array so as to avoid scaling computations
during simulations. Care must be taken since the B table
contains 1/tau rather than the beta values. It is recommended,
therefore, that both alpha and beta be adjusted simultaneously
and identically. Alternatively, the scaletabchan function may
be used to scale the two tables in such a way as to scale
alpha, beta, tau, or the steady state activation (minf).
The CALC_ALPHA, CALC_BETA, and CALC_MINF functions
The CALC_ALPHA, CALC_BETA, and CALC_MINF actions are used with
calls of the form
y = {call <element> CALC_ALPHA <X/Y/Z> <x-value>}
in order to access values of alpha, beta or m_inf (the steady
state activation, alpha/(alpha + beta)) for the specified gate
(X, Y, or Z) and a particular value of the independent
variable. This feature is most often used for making plots of
these quantities. Note that the activation time constant can
be calculated from tau = 1/(alpha + beta).
Example: see Scripts/neurokit/prototypes/traub91chan.g
See also: Interpol documentation (Tables), scaletabchan, setupalpha,
setuptau, tweakalpha, tweaktau, hh_channel, tab2Dchannel
Click here to get the file
ebook "Neural Networks as Cybernetic Systems" (3rd edition)