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.

On Feb 19, 7:18 am, dsummers...@gmail.com wrote:
> 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.

Think about the scale, and the distances involved. They are very, very
short.
As a result, you don't have to move things far, and a *lot* of
attempts can
take place in a very short time. In fact, you can argue that 1000bp/s
is
slow - if things were better arranged the process could be much
faster.
Compare with modern electronics, which operates a million times
faster,
on a similar scale.

It may look like a reverse entropy process to you, but iirc, the
energy is
coming from two of the phosphate groups being removed from
nucleotide triphosphates by hydrolysis.

Peter Trei

(dsummerstay@gmail.com) 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

On Tue, 19 Feb 2008 04:18:06 -0800 (PST), dsummerstay@gmail.com wrote:

>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?

The same way it does in your imagined bag of magnets, only about a
million times faster. The mechanism is the same, and the DNA bases
are probably bouncing around due to brownian motion at about the
same speed you are imagining the magnets bouncing around, but the
DNA bases only need to move a dozen or so *nanometers* between each,
"Do I fit in this spot at this angle? Nope; time to bounce off and
try again", whereas your thought-experiment magnets have to move a
dozen or so millimeters each time.

The smaller a thing is, the faster it will do whatever it does. And
molecules are really, really, really small.

So if you find it necessary to imagine things being a million times
larger than they actually are to visualize what's going on, you have
to keep in mind that you have similarly magnified the time scale.


--
*John Schilling * "Anything worth doing, *
*Member:AIAA,NRA,ACLU,SAS,LP * is worth doing for money" *
*Chief Scientist & General Partner * -13th Rule of Acquisition *
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dsummerstay@gmail.com skreiv:

> 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.

Frequencies are size-dependant.

In general the relationship between many forces is counterinituitive
when the size changes by many magnitudes.

In the range of sizes we're used to dealing with, say 10g to 100kg our
intuition is usually pretty close on. People used to dealing with the
much larger or much smaller develop intuition for these things too.

At -HUGE- sizes gravity is crushing and dominates movement of objects,
planets, suns and galaxies move primarily dominated by the gravity
between them. Inertia is very high.

At 1000s of tons, inertia is still a bitch. A supertanker responds very
slowly to actions of the propeller and rudder, it needs -minutes- to
stop or accelerate. Gravity is strong enough that only sea-going
vehicles are able to be mobile at all at this size.

At 1 ton or similar we're talking a car or elephant. It still has
inertia, but a car driving at supertanker speed can stop in a second in
a few short meters. Gravity is a problem. Animals this size have
problems getting of the ground at all, I don't think a elephant is
capable of jumping. It needs a second or thereabouts to take a single step.

At a few kgs you're talking a cat, gravity is less of a bitch: despite
having a -much- lower percentage of its body-weight spent for skeleton a
cat can jump or fall many times its body-height without suffering injury
(try dropping a elephant from 5-times-body-height) Frequencies are much
higher, a cat can take 10 steps or so in the time where an elephant
manages one step. A elephant built like a cat would not be able to stand up.

At a g or so you're talking a insect. Beating your wings 100 times in a
second is fine at this size. Try imagining an eagle beating wings 100
times in a second, an utterly ridicolous idea.

So short answer: 1000 times a second IS very slow when you're talking
something on the scale of a single molecule.

Behind it all is the square-cube law: If you double the size of
something in all dimensions, then the cross-section of bones and muscles
go up by a factor of 4 (2*2) but the *mass* (and thus inertia and
gravity) go up by a factor of 8 (2*2*2)



Eivind Kjørstad

What great answers! Thanks, everyone.