[Neuroscience] Re: Decay constants. What does "weighted" mean?

Imre Vida via neur-sci%40net.bio.net (by I.Vida from bio.gla.ac.uk)
Thu Jan 15 12:40:10 EST 2009

On Thu, Jan 15, 2009 at 09:17:00AM -0700, r norman wrote:
> On Thu, 15 Jan 2009 01:01:28 -0800 (PST), Bill
> <connelly.bill from gmail.com> wrote:
> >Hi,
> >
> >Synaptic events decay with an (bi)exponetial function. You can of
> >course report the decay constant, which I understand, but what do
> >people mean when they refer to the weighted decay constant?
> >
> >Thanks.
> When a function does not show simple exponential decay, but rather has
> several terms each with a different time constant, then each term has
> a "weight" associated with it
>    a exp(-t/t1) + b exp(-t/t2) 
> where t1 and t2 are two time constants and a and b are the respective
> "weights".

from this, the weighted decay time constant is:
 tw = (a*t1+b*t2)/(a+b)
it is a simplification, to describe the "speed" of 
the decay with a single value and enable the comparison 
of "events" with different decay kinetics

i guess when you say synaptic events, you mean E/IPSCs 
i.e. currents. Their decay kinetics is dependent on when the 
channels close, deactivate or desensitize.


> That is the usual meaning, but describe the use of the term in
> context, or better, the citation with a material and methods sections
> talking about how to calculate the values, and I can describe it
> better.
> Note:  an RC circuit, of course, has a simple exponential decay but
> synaptic decay is complicated because of the spatial decay
> superimposed on the temporal decay.  That is, the partial differential
> equation of the cable equation of the dendritic tree is rather
> different from the simple differential equation of an RC circuit.  Of
> course, lingering synaptic activation also can complicate the decay
> pattern.  That means that synaptic decay is not simple exponential
> decay.
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