Duh, what I just said was tautologous; of course any simply-connected linear DNA with two ends is never "knotted" in the mathematical sense! More accurately, linear DNA tends to kink/clump up in a very local way -- getting shorter and fatter, while becoming more of a _space-filling_ curve in between the ends. If you color the entire length of a double strand like the visible color spectrum, where one end is violet and the other end is red, then even in its kinked/clumped form, the DNA would have smooth shadings of color. I.e., portions of the DNA strand that are far away from each other when the strand is stretch out straight are still far away from each other even in the kinked/clumped form. What I am saying boils down to the following: If you saw a DNA linear double-strand in its kinked/clumped form, and could find the two ends and grabbed them & joined them, you would have a greater than even chance of forming a simple loop (unknot), with the near certainty that if it wasn't an unknot, it would be a trefoil knot. This is the cool part: nature seems to go to a lot of trouble to make sure that this type of DNA doesn't get any more knotted than this. At 02:06 PM 12/25/2012, Henry Baker wrote:
Ok, I think I see a potential definitional problem.
"Long strands of DNA floating in a cells nucleus can easily become tangled, just as a long extension cord does when left in a heap."
<I>. Let's suppose that one end of the extension cord is plugged into the inside wall of a rigid sphere, and that the other end is attached to another point on the inside wall of a sphere, and the entire length of the cord lies within the sphere and is (of course) restricted to remain within the sphere.
Assuming that the extension cord was originally "untangled", meaning that it could slowly contract like a rubber band until it becomes a chord on the sphere, then no normal "tangling" you can do to the cord (so long as you never, ever unplug either end) will change this "untangled" property.
<II>. However, if you picked up two ends of an extension cord tangled at random and then attached them to the inside of a rigid sphere as above, there is no guarantee that the tangle could ever be untangled without unplugging at least one end of the cord.
I would define situation <II> where it is actually impossible to untangle the cord as "knotted", whereas situation <I> is merely "tangled".
In real life, of course, even untangling a cord in situation <I> may be extremely difficult w/o unplugging it, but it isn't impossible.
At 12:32 PM 12/25/2012, W. Edwin Clark wrote:
In this article it is explained how some "circular" DNA knots are obtained: