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Re: centrifuge exercises



At 10:49 AM 11/5/00 -0500, Ludwik Kowalski wrote:

The problems you described are good and worth discussing
in the context of what we teach.

I'm glad you like 'em.

Are you saying that this is not true for the centrifuge (because objects
are microscopic)?

By "centrifuge" I assume you mean biology-lab centrifuge. The utterly
macroscopic centrifuge at the Air Force Academy is a perfectly fine
centrifuge if you ask me. "Microscopic" isn't the real issue; the issue
is if we have particles moving through viscous liquids we need to account
for buoyancy and viscosity.

Earlier you had declined repeated suggestions to invoke Stokes law of
viscosity because it hadn't been covered yet. Since you now seem to have
changed your mind about that, we can begin to address the bio-lab centrifuge.


suppose that everything up to chapter 10 has
already been learned.

Roger.

Use mud in water (instead of blood)

Avoiding blood is good. Blood is complicated.

But mud is complicated, too. We know (from electrophoresis) that your
typical clayey mud particles are charged. Colloid physics is more than
your first-year non-major can cope with.

A uniform initial distribution of radii, from 0.0001 to 0.01 cm is probably
acceptable for a simple typical centrifuge problem.

The large end of that range is waaaaay too large. 100 microns? You might
as well use buckshot.

Biologists are typically going after smaller things.

At 02:15 PM 11/5/00 -0500, Ludwik Kowalski wrote:
For very small
particles (r<0.1 mm) terminal velocity is reached over
very short distance and the time to cover 25 cm is
practically equal to 0.25/vt.

In a real bio-lab centrifuge, the distance particles travel during
sedimentation is more like 1cm, not 25cm. This active region is _located_
maybe 15cm from the spindle. It is important not to confuse these two
distances.

So it would be better to divide the following numbers by a factor of 25:

r=0.1 mm --> time=6.75 seconds
r=0.01 mm --> time =675 secends
r=0.001 mm --> t=18.75 hrs
r=0.0001 mm --> t=1875 hrs = 78 days
r=0.00001 mm --> 21 years, etc.

Can somebody go one step further and show by how
much these times are reduces at 100 rev/sec ?

6000 RPM on a 15cm radius is about 6000 Gees. So divide the foregoing
numbers by a (further) factor of 6000. I get:

r/mm settling_time/sec
0.1 4.50E-05
0.01 4.50E-03
0.001 0.45
0.0001 45.
0.00001 4501.
0.000001 450180.

==================================

For things with the density of protein, the following formula appears to be
a good predictor of sedimentation coefficient given molecular weight over a
wide range:

(sed_coeff/Svedbergs) = 0.0025 * (MW/Daltons)^(2/3)

I inferred this from the data in ref (3).

=====

If I wanted to cobble up a nice exercise, I would try something like this:

Assignment: Choose suitable values for XXX and YYY in the following:

Scenario: Two-step differential settling, with the goal of collecting
ribosomes. Settling occurs in tubes with relevant dimension
1cm. Eukaryote ribosomes have a sedimentation coefficient of 80 Svedbergs.
Step 0: Put cells in the blender on "high" :-)
Step 1: In tube #1, let settle under conditions XXX to settle out
everything larger than ribosomes while leaving most ribosomes (and smaller
stuff) in suspension.
Step 2: Transfer the supernate to tube #2 and let settle under conditions
YYY to settle out the ribosomes while leaving most everything smaller in
suspension.

Multiple choice:
1) Which of the following are suitable choices for XXX?
2) Which of the following are suitable choices for YYY?

a) 1 Gee for 45 minutes
b) 1500 Gee for 30 minutes
c) 25,000 Gee for 3 hours
d) 50,000 Gee for 20 hours


I like this exercise because
a) It is completely non-hokey.
b) It is not grungy, i.e. not unduly burdensome. A student who knows
what is going on can solve it in less time than it takes to tell about it.
c) Making it multiple-choice makes it easier to grade the
answers; there is no doubt about what the right answer is. The
non-multiple-choice version would suffer because
-- the full solution-space is two dimensional
-- the boundary of the solution-space is a bit fuzzy
and I don't want to argue about the details.



================

References
1)
http://www.columbia.edu/cu/biology/courses/c2005/faq99/aca1.html#38
2)
http://xnet.rrc.mb.ca/martins/Biochem%202/RNA1.htm
3)
http://www.foresight.org/Nanomedicine/Ch03_1.html