In article <7tbo01$2ml$1 at nnrp1.deja.com> , hursun at math.ewha.ac.kr writes:
>Isn't this important that if I observe the membrane with Na+ channel
>and pumps more often than the pumping frequency..then I do not see then
>in equilibrium at that moment...(for more long view,,it's only
>equilibrium).but cells with only K+ channels,,it does not depend on how
>often I see them...
>Actually this was what I thought about the difference. But ..... even
>thogh this is not the case....does it have any importance in biology?
>I mean the averaging time scale..
I'm not sure I understand your question completely, but it seems to me
that you are asking whether "equilibrium" and "steady-state" depend on
the time scale over which the observation is made.
I would say "yes" and "no", in both cases. On the short time scale, one
may see lots of fluctuations and drift and conclude that the system is
not at steady state (or equilibrium) even if it truly is. For example,
suppose you measure the openings of an ion channel for ten seconds, and
plot the number of openings (or the open times or whatever) against the
time in seconds that you are collecting data. This plot will probably be
very wiggly (because ion channel gating is random), and you might
potentially see a lot more (or less) openings later in the record. You
might look at this and conclude that the channel is experiencing an
"activation phase" in which its opening rate is slowly increasing, or in
which it is moving from states with low open probability to higher ones.
But if you repeat the measurement for an hour, now the plot might still
be wiggly, but each upward wiggle is counter-balanced by an equivalent
downward wiggle. So the average opening frequency (over an hour) would be
a flat line (i.e., steady-state).
On the other hand, suppose there is more than one channel in your patch,
and for some reason the channels have a tendency to "die" over long
recordings (say, each channel has an average functional lifespan of
fifteen minutes). This time, the ten second recording might look pretty
flat when compared with the downward drift that you see in the hour long
recording. So you might conclude that even over an hour the channels are
not at steady-state. However, if you restricted yourself to only looking
at five minute windows, most of these would look pretty stable (we call
this "stationarity").
So yes, the conclusion you come to about steady-state (or equilibrium)
depends somewhat on the averaging timescale (when dealing with random and
especially biological processes).
BUT neither of these scenarios helps you to decide whether the system is
just at steady-state or at true thermodynamic equilibrium. To do that (in
the ion channel example) you might do something like show that the record
gives the same frequency of transitions between various states when
viewed either backwards or forwards in time (e.g., short openings->medium
openings-> long openings->medium->short->medium->long, etc...). This is a
test for so-called "microscopic reversibility", and any system at
thermodynamic equilibrium is supposed to follow this behaviour. However,
if instead you noticed that the channel tends to follow a circular
pattern of gating (e.g., short openings->medium openings-> long
openings->short->medium->long, etc...) this would suggest that some
energy flow is at work to maintain this net movement through the gating
scheme in one particular direction.
In practice, data that is adequate for testing these mechanism on ion
channels is extremely hard to come by (because you need huge amounts of
data for statistical testing). Examples of both types of mechanism exist
in the ion channel literature.
Cheers,
Matt Jones
