Definitions for the following terms?

Richard Norman rsnorman at mediaone.net
Tue Jul 10 16:51:05 EST 2001


On Tue, 10 Jul 2001 16:23:41 -0400, "Isidore"
<isidore at mailandnews.com> wrote:

>Hi everyone,
>
>    I'm a high school student trying to read a neuroscience paper and
>understand it well. There are some keywords listed at the top of the page
>that I'm not exactly clear on. They aren't explicitly alluded to in my
>textbook (although perhaps they are by another name).  If someone could help
>clarify these for me, I'd appreciate it.
>
>renewal process: Is this just referring to the process the neuron has to go
>through before it fires another action potential (absolute refractory
>period, relative refractory period, etc.?)
>
>integrate-and-fire: Is this just referring to the neuron firing when
>threshold is reached? Why do they call it INTEGRATE-and-fire? Is there any
>alternative to integrate-and-fire? What is a leaky integrate-and-fire
>neuron?
>
>interval distribution: Is this just the lapses between the action
>potentials?


Obviously, you are reading a paper dealing with spike train analysis,
whether on real axons or simulations.  This type of stuff can get
quite hairy indeed. 

There are a number of general points which you should know.  First,
many papers in neurobiology are exceptionally specialized and are very
difficult to understand, even by specialists. And that is even when
they are well written.  All too many are not!  If this is your first
venture into the real scientific literature, it can be horrible shock.
Just stick with it.  It does get easier after a few years.  Second,
(although I shouldn't reveal trade secrets so early to an initiate)
most experienced scientists learn how to fake it.  That is, it is not
necessary to understand evey last detail if the paper is not really
exactly the type of thing you, yourself, do.  You just learn to get
the general gist of it.  Then gradually you learn to get more and more
of the details.  Finally you learn to guess at all the other details
the pass you by. 

Now for your particular questions.  The key-words you found at the top
of the paper are useful for indexing purposes -- showing what the
general subject matter is.  The most important is interval
distribution.  The intervals, as you guessed, are the time periods
between action potentials.  I would guess the paper is concerned with
analyzing (or predicting) the statistical properties of the
inter-spike intervals.  For example, in a completely random process,
where the probability of a spike occurring at any one time is the same
as it occuring at any other time and where that probability does not
depend at all on how long it has been since the last action potential,
in that case the intervals will show a particular mathematical
distribution called Poisson.  But presumably if the axon is
transmitting information, then it would not be firing "randomly" and
the spike distirbution might contain the key to the type of
information being transmitted.  It might also help understand the
process that led to the production of that particular spike train.

Integrate-and-fire represents a model for how the neuron generates the
action potentials.  Essentially, the "cable properties" of the
dendritic tree (the space and time constants produced by the cell
resistance and capacitance) will add up all the excitations and
inhibitions occuring recently (temporal integration) to see if the
cell reaches threshold.  It is leaky because the effects wear away
after a while.  I find www.google.com a good place to search for
technical material.  It produces remarkably good hits.  So a search
for "integrate and fire" quickly produced an excellent paper by
Stevens and Zador at
http://www.sloan.salk.edu/~zador/rep_fire_inc/rep_fire_inc.html.

A renewal process is a particular kind of statistical process.  The
word "renewal" doesn't have anything to do with refractory period --
it is a technical term.  This one is hard to search because you end up
getting web sites dealing with the process of renewing all sorts of
agreements and licenses.  But if you search "renewal stochastic
process" you find http://www.puc-rio.br/marco.ind/stoch-a.html which
gives you some definitions.  Of course this one gives you the
gobbledygook "Any counting process which is generated by an iid
(independent identically distributed) sum process (Tn) is called
renewal counting process."  But that is the nature of the beast. The
mathematics of random processes tends to be a graduate level course
for mathematics and statistics students (or those engineers and
physicists working in noise or random processes).

So keep working at it.  And keep asking questions! 





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