## AlphaSynapse and Alpha Function

The basics of how to develop, test, and use models.
shailesh
Posts: 104
Joined: Thu Mar 10, 2011 12:11 am

### AlphaSynapse and Alpha Function

This is more of a general query hence posting here. I was having some confusion over the way the alpha function is implemented for modeling current/conductance.
This is what I have seen at different places:

1>> Some books (e.g. Jack, Noble & Tsien, 1975) and papers (e.g. Purves, 1976) implement alpha-function as:
I(t) = (alpha^2) * t * exp(-alpha*t)

2>> Rall (1967) suggests something of the form:
f(t) = (t/tp) * exp (1 - t/tp)
i.e. f(t) = (alpha*t) * exp (1 - alpha*t)

3>> NEURON, for its AlphaSynapse, uses (let tact = 0):
g(t) = gmax * (t/tau) * exp(-(t-tau)/tau)
i.e. g(t) = gmax * (alpha*t) * exp(1 - alpha*t)

The latter two are basically the same. But I could not figure out why/how the first one is used/dervied?
Does it have anything to do with modeling current or the underlying conductance? Are they equivalent in some manner?

p.s. the documentation for AlphaSynapse might need a slight correction:
this has the property that the maximum value is gmax and occurs at
t = delay + tau.
I suppose it should be:
t = onset + tau

Thanks!
ted
Posts: 5822
Joined: Wed May 18, 2005 4:50 pm
Location: Yale University School of Medicine
Contact:

### Re: AlphaSynapse and Alpha Function

What are the peak amplitudes of functions 1 and 2?
What are their integrals?
Does it have anything to do with modeling current or the underlying conductance?
No.
this has the property that the maximum value is gmax and occurs at
t = delay + tau.
I suppose it should be:
t = onset + tau
True, that's an error that should be corrected. Contrary to rumors, occasional errors have not been deliberately inserted to see if anybody is reading the documentation or the comments in the source code.
shailesh
Posts: 104
Joined: Thu Mar 10, 2011 12:11 am

### Re: AlphaSynapse and Alpha Function

What are the peak amplitudes of functions 1 and 2?
They appear to only dictate the shape, as peak amplitudes have not been explicitly stated (nor used in calculations). Reason, I suppose, being the study was more to do with regards to the time courses of junction potentials, and so amplitudes were normalized.
e.g. for function 2 (Rall, 1967), all it says is F(T=0) = 0.0 and F(T=tp) = 1.0
What are their integrals?
I am not quite sure. Just came across these equations, and no derivations were provided. And worse, no references to its origin.
Can't figure out the rationale for use of the 'modified' form (function 1) of alpha function.

p.s. We could have a different section on the forum for documentation errata (not sure if we already have it). Might make it useful to collate info whenever its to be updated.
ted
Posts: 5822
Joined: Wed May 18, 2005 4:50 pm
Location: Yale University School of Medicine
Contact:

### Re: AlphaSynapse and Alpha Function

My questions were meant as suggestions to dust off the old calculus and derive the necessary results. "Left as an exercise for the reader" as Johnson & Kiokemeister would say.
shailesh
Posts: 104
Joined: Thu Mar 10, 2011 12:11 am

### Re: AlphaSynapse and Alpha Function

As far as I can tell, they just appear to be different ways of obtaining the same (or extremely) similar shape.
If results are normalized, there doesn't seem to be anything to tell them apart. Pilot simulations seem to suggest the same.