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

r norman via neur-sci%40net.bio.net (by r_s_norman from _comcast.net)
Thu Jan 15 17:46:38 EST 2009

```On Thu, 15 Jan 2009 18:40:10 +0100, Imre Vida <I.Vida from bio.gla.ac.uk>
wrote:

>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".
>>
>> 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.
>>
>
>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.

Yes,  I didn't combine the separate decays into a single "weighted"
value.

If the synaptic events are, indeed, the currents  then the various
decay kinetics do relate to the kinetics of decay of the channel
closing.  I was assuming potentials, in which case the membrane cable
properties are the most important aspect, something that  will
ordinarily completely obscure the channel kinetics.

So it really becomes important to see what the original authors are