Routine Name: setupalpha
Description: Sets up A and B tables of voltage-dependent gates based on
generic equations describing the form of the alpha and beta
rate functions.
Usage: setupalpha channel-element gate AA AB AC AD AF BA BB BC BD BF \
-size n -range min max
channel-element This must be a tabgate or a tabchannel i.e.
a voltage-dependent gate or channel with
tabulated activation functions.
gate The name of the gate (must be X, Y, or Z).
AA-AF Coefficients A to F of the alpha table
(see below).
BA-BF Coefficients A to F of the beta table
(see below).
-size n Number of divisions in the table
(default = 3000).
-range min max Range of the table (default: min = -0.100;
max = 0.050).
This routine makes it easy to set up the A and B tables of
tabulated channels or gates (tabchannel or tabgate objects)
when the equations describing the rate constants alpha and
beta are of the form:
y(x) = (A + B * x) / (C + exp((x + D) / F))
Many standard channels have alpha and beta parameters that can
be cast into this form. In these cases to set up the tables
we can simply call setupalpha with the parameter values as
arguments to the function. Since there are both alpha and
beta variables, we use the coefficients AA-AF to refer to the
alpha variable and BA-BF to refer to the beta variable.
setupalpha calls the TABCREATE action of the tabchannel or
tabgate to allocate tables with n divisions (n + 1 entries)
representing x values from min to max. It then evalutes the
functions at these points to fill the tables.
tabgates have tables for the alpha and beta rate variables, so
these alpha and beta values are used to directly fill the
tables. The gates of a tabchannel each have an A table that
holds alpha values, and a B table that contains alpha + beta.
These tables are filled with A = alpha and B = alpha + beta.
The tables are by default set up in "no interpolation" mode,
which means that the process of finding the correct table
value is simply a lookup operation. With 3000 divisions in
the table (i.e. the table size is 3001) the lookup usually
provides sufficient accuracy. If not, you can override this
behavior; see the tabchannel documentation. The range of the
activation variable is between -0.100 and 0.050 by default.
This is adequate for most voltage-dependent channels, but
can be overridden using the -range option.
Example: from Scripts/neurokit/prototypes/traub91chan.g:
create tabchannel Kdr_hip_traub91
setfield ^ \
Ek {EK} \ // V
Gbar { 150 * SOMA_A } \ // S
Ik 0 \ // A
Gk 0 \ // S
Xpower 1 \
Ypower 0 \
Zpower 0
setupalpha Kdr_hip_traub91 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
This command sets up the X gate (activation gate) of Traub's
delayed-rectifier potassium channel (Kdr_hip_traub91).
SOMA_A and EREST_ACT are constants defined in the script
file. Note that the C value for the A table (AC) is -1; this
can cause problems in general but does not cause any problems
here (see below).
Notes: For tabgate elements, which represent only a single gate, the
"gate" argument is ignored, but it should still be given as
X, Y, or Z. The setuptau command is similar to setupalpha,
but uses the state variables tau and minf instead.
If the alpha and beta rate constant of your channel cannot be
described using the above equation, you must fill the tables
with one of the other methods described in the tabchannel
documentation, or The Book of GENESIS, Chapter 19 (2nd ed.).
The rate equation described above has a removable singularity
when C = -1 at the point x = -D (which is, unfortunately, a
common case). In this case the routine may generate
inaccurate results due to roundoff errors. We STRONGLY
RECOMMEND that if you must use a C value of -1 you check the
resulting activation curves by using Neurokit (in the "Edit
Channel" mode) to see if they look reasonable. If they do
not then you will have to define the channel using a script
function as mentioned above. Such a function will result in
a slower setup time for the channel but will be much more
accurate.
See also: tabchannel, tabgate, setuptau, tweakalpha, tweaktau, Tables