question related to neuron spiking

[Xiaoshen Li]

Matt Jones wrote:
> 
> Your example of potassium chanel activation "brings the membrane
> potential back" is on the right track. If you think more along these
> lines, you'll be able to figure out AHPs and ADPs for yourself.
> 
> Some hints:
> 1) Does K-channel activation really "bring the membrane potential
> back"? Or does it take the potential to somewher *different* than the
> resting potential? For example, a typical neuron may have a resting
> potential of
> -60 mV? Is this where the voltage goes immediately after a spike, or
> does it go somewhere else (i.e., where are the K-channels *trying* to
> take the membrane potential?)? How do you calculate this?
> 

Suppose the reversal potential of K ion is -70mV, calculated from Nerst 
Equation, mainly determined by the ratio of K ion concentrations inside 
and outside of the neuron membrane. So opening of K-channels will try to 
v-clamp to -70mV. It is even lower than the membrane resting 
potential(say, -60mV). So Vmem will overshoot downwards a little bit. 
This overshooting is called "afterhyperpolarization", or AHP.

More specifically, the curve of AHP starts from the point where Vmem 
equal to Vrest when Vmem decreasing from the action potential peak, ends 
at the point where Vmem is the most hyperpolarized. Correct?
> 2) If you answered the last question correctly, you should now know
> why K-channel opening causes an AHP.  How would you instead cause an
> ADP? (you will have to think slightly outside of the HH equations to
> figure this out, but not very far outside).
> 
After-depolarization(ADP):

Now I guess, following the discussion about afterhyperpolarization 
above, the membrane potential will return(=rise) to its resting membrane 
potential. The resting membrane potential is determined by the neuron's 
membrane leakness and other a few opening channels.  This part is called 
after-depolarization. Correct?

More specifically, the curve of ADP starts at the end point of AHP, ends 
at the point where Vmem backs to Vres. Compared to AHP, ADP takes much, 
much longer time and the slope is much shallow. Correct?

If I am correct above, I know this phenomenon. I just took it for 
granted. Never thought it has some significant meaning. I read in the 
paper "Neurons showed spike after-depolarizations along with doublet or 
burst firing...". I am confused. Any neuron doesn't show 
after-depolarization?

> 3) Regarding the "monophasic" part, that means that there are no
> sudden jumps or inflections during the decay of the AHP. 
Question: I have never seen any sudden jumps or infections happening 
within a spike. Could you give me more information?

In some
> cells, there are biphasic AHPs, that decay as the sum of two
> exponential components. Yes, this shape does tell you something
> significant about the underlying mechanisms. What would you have to do
> to the HH equations that would produce a biphasic AHP?
> 
If I am correct about the curve of AHP above, fitting this curve with 
one or two exponential functions determines if it is mono-phasic or 
bi-phasic. But I don't see how pure Hodgkin-Huxley mechanism will 
produce a mono-phasic AHP with time constant tao. And what this tao 
correspond to which parameter in HH model? I don't know how to change 
the model to have biphasic AHP.

Thank you very much.

Best,
Xiaoshen