(dsummerstay@[EMAIL PROTECTED]
) writes:
> How is it possible for DNA to reproduce at the speeds it does? DNA
> bases find their place at a rate of up to 1000 base pairs per second
> at a replication site. I have a hard time picturing this. Imagine a
> string encrusted with magnets, thrown into a bag of short magnetic
> clusters and shaken rapidly. I can imagine, if the design was clever
> enough, that occasionally a cluster would find its proper place at the
> end of the string, as the clusters got knocked around and one just
> happened to land at the right angle to get knocked into the right
> place to join at the end of the string. But this would be a very slow
> process. Most of the time, the clusters would block each other by
> fitting in a not quite perfect way (a local energy minimum) rather
> than instantly finding a perfect fit (a global energy minimum). How
> does it happen so fast in the cell?
> If you watch visualization movies of the process, it looks like a time-
> reversed video, because it is so clearly going from a disordered state
> (base pairs floating nearby) to an ordered state (a DNA molecule) very
> quickly.
Just for fun, a few numbers. The mean molecular weight of a DNA base
molecule is about 130 g/mol or 2.17x10^-25 kg, and kT at 300 K is
4.14x10^-21. Equating the kinetic energy of the base molecule to 1.5kT
gives a velocity of 239 m/s at room temperature.
If I rather crudely represent the motion of the base molecule in water as
a
random walk with a path length of 1 nm, the collision frequency works out
to 2.39x10^11 per second. The mean distance travelled on a random walk in
one second is then (1 nm) x sqrt( 2.39x10^11) or 4.88x10-4 m.
If we take an arbitrary point and draw around it a sphere with this
radius, than any base molecule within that sphere is capable of reaching
the central point within one second. This sphere has a volume of
4.9x10^-10 m^3.
I'll guess the concentration of base molecules at 1 millimolar, so that
there are 6x10^23 molecules per m^3. Then our "one-second" sphere contains
6x10^23 x 4.9x10^-10 or about 3 x 10^14 base molecules, all within reach
of the central point in one second.
If these estimates are anything like right, it's not too surprising that
1000 of them actually make it.
--John Park
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