Object Type:
tabchannel
Description:
Hodgkin-Huxley type voltage activated channel with
tabulated
equations.
Author:
E. De Schutter, Caltech (1/91)
----------------------------------------------------------------------------ELEMENT PARAMETERS
DataStructure:
Size:
tab_channel_type
[in src/olf/olf_struct.h]
168 bytes
Fields:
activation
Gk
Ik
Ek
Gbar
X
Y
Z
channel activation
channel conductance
channel current
channel reversal potential
channel maximum conductance
value of X gate; optional gate, X=m
value of Y gate; optional gate, X=h
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
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 CHECK PROCESS
RESET INIT
Messages:
VOLTAGE
EK
CONCEN
voltage
Ek
concen
[membrane voltage of compartment]
[reversal potential]
[ion concentration sent to
channel]
DOMAINCONC Ik
scale
[ion current from another
channel, to
be multiplied by scale, and
divided by
ADD_GBAR
offset
surface field]
[increment to be added to Gbar]
----------------------------------------------------------------------------Notes:
dependent
Tabulated hh-like channel.
The standard voltage
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 computation 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 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 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 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
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