discussion on variability and neural codes

[Bill Skaggs]

Marius Usher and Martin Stemmler write:

> Perhaps the most crucial question in the study of cortical function
> is whether the brain uses a mean rate code or a temporal code.

I would like to argue that we should refrain from putting the question
in these terms, because it is not productive.  But first I should say
that my criticism applies only to this one sentence that Marius and
Martin wrote, not to the rest of their presentation, which I think was
quite sophisticated and insightful.

The problem with posing the question in terms of a mean rate code
versus a temporal code is that the reality is clearly somewhere in
between.  A mean rate code is one in which shifting the time of an
action potential makes no difference; a temporal code is one in which
shifting the time does make a difference.  For any code actually used
in the brain, though, shifting the time of an action potential will
make a difference if and only if the shift is sufficiently large.  This
is actually pretty obvious:  shifting a spike by 1 nanosecond surely
won't make a difference anywhere in the brain, but shifting by 1 year
surely will make a difference everywhere.

The right question to ask is how large a shift it takes to make a 
difference.  We can think of this in terms of a plot of the 
following form:


   | Effect
   |                             ***************************
   |                  ***********
   |           *******
   |        ***
   |      **
   |    **
   |   *
   |  *
   | *
   | *
   |*
   |*                                                          
   |_____________________________________________________________
                                                 Spike Time Shift

Thus, for any sort of imaginable code, the effect of shifting a spike
will increase linearly for very small shifts, and will eventually
saturate at a level beyond which further time shifts have no greater
effect.  (The saturation level is equal to the effect of deleting the
spike entirely.)  Of course, complicated things may happen in between.

Instead of asking whether we are looking at a mean rate code or a
temporal code (which is a meaningless question), we should ask what the
shape of the time shift-vs-effect curve is, and in particular, what the
largest and smallest time constants are.  Note that, although the shape
of the curve may change if the effect is quantified in a different way,
the time constants are likely to remain similar.

In some parts of the brain, the auditory system in particular, time
constants in the submillisecond range are clearly present.  In a
wide range of systems, though, including Bialek's fly motion cells,
Wyeth Bair's MT cells, and the hippocampal place cells our group has
been working with, the smallest time constants seem to be in the 
10--20 msec range.  As a cynic might perhaps expect, this range is
perfectly positioned for both the mean rate and temporal coding camps
to seize on as evidence to support their views, thereby confusing the
issue almost beyond hope.  I think we will make better progress in 
understanding neural coding if we can get beyond this simplistic
dichotomy.

In summary:  Ask not whether 'tis a rate code or a time code; ask
rather what the time constant is.

	-- Bill