AHP conductance descriptions

[Ilya Rybak]

Dear Connectionists,

I am developing models of respiratory and baroreflex neural networks
on the base of H-H style model of single neuron. I have a problem
with description of AHP conductance, that play a very important role
in my models. I would be very thankful to everybody for any help.

The problem consists in the following.

Let's consider the description of AHP conductance in the paper of
Yamada et al."Multiple channels and calcium dynamics"(In Methods in
oNeuronal Modeling.Eds. Koch and Segev, The MIT press, 1989,97-133.)
In the page 132, you can see for AHP conductance that

             tau=1000/(f(Ca)+b)                                (1)

             m=f(Ca)/(f(Ca)+b)                                 (2)

In the page 133, you can see that

             f(Ca)=1.25*10^8*[Ca++]^2   and b=2.5              (3)
                        -----
Ca is measured by mM.                                          (4)

In the page 132, you can also see that

 "the midpoint for m is 44.7 nM and for m^2 is 69.5 nM"        (5)

It is very simple to chech that (1)-(4) do not correspond to (5).
I think, that it is mistake. To correct this mistake we have to
change (3). There are two ways for this:

1)      f(Ca) is the same as in (3), but b=0.25                (6)
                                         -------
2)      f(Ca)=1.25*10^9*[Ca++]^2  and b is the same as in (3)   (7)
                 -------- 
I do not know what is correct (3) or (6) or (7). But the behavior of
the behavior of my model depends on this very strong.

I have tried to compare the discription of AHP conductance in Huguenard's and 
McCormick's Manual for VClamp and CClamp. In the page 28 of the Manual
the authors refered to the same paper and wrote:

       alfa=1.2*10^9*[Ca++]^2  and betta=0.001                   (8)

Taking into account that 

      f(Ca)=alfa*1000   and  b=betta*1000                         (9)


and that Ca is measured in M                                     (10)

we can get the following

      f(Ca)=1.2*10^6*[Ca++]^2   and b=1                          (11)
               -------
This is absolutely different from (3) as well as from (6) as well as from (7).
The expresions (3), (6), (7) and (11) are too different. Because of this
the behavior of my neuron and network models is absolutaly differnt depending
on which one AHP description I use. I cannot go ahead without finding out
which one of descriptions is correct. I will be very tankful to everybody for 
any explaination of this mysterious.

Sinceraly,

Ilya Rybak
Dept. of Neuroscience University of Pennsylvania and
Neural Computation Group at DuPont Com.
ilya at cheme.seas.upenn.edu