Re: [math-fun] J Borwein's sig
The amazing thing about DNA is that even though it is incredibly long, it never seems to "knot". I guess that if it ever does get knotted, the whole cell commits suicide (or at least tries to -- perhaps a source of cancer?) Some relatively small bacterial and mitochondrial DNA are circular (except when being copied), which probably aids in keeping them from knotting. At 04:47 PM 12/24/2012, Fred lunnon wrote:
On 12/25/12, Bill Gosper <billgosper@gmail.com> wrote:
Awful thought: What is the expected time at which a 3D random walk first becomes "knotted"? (W.r.t. pulling on the ends.)
Bearing in mind that the ends may in general lie deep within the convex hull of the walk, perhaps this question requires rather more careful definition ... WFL
Not at all! DNA does indeed become knotted; most notably, this is inevitable when a circular chromosome gets replicated to create two daughter chromosomes, whose knotting is forced by the helical structure of DNA. The cell's solution is a class of enzymes called topoisomerases, which serve only to break the phosphate backbone of one strand, pass the other through it, and then repair the broken one -- a topology-only chemical reaction. --Michael On Dec 25, 2012 7:08 AM, "Henry Baker" <hbaker1@pipeline.com> wrote:
The amazing thing about DNA is that even though it is incredibly long, it never seems to "knot".
I guess that if it ever does get knotted, the whole cell commits suicide (or at least tries to -- perhaps a source of cancer?)
Some relatively small bacterial and mitochondrial DNA are circular (except when being copied), which probably aids in keeping them from knotting.
At 04:47 PM 12/24/2012, Fred lunnon wrote:
On 12/25/12, Bill Gosper <billgosper@gmail.com> wrote:
Awful thought: What is the expected time at which a 3D random walk first becomes "knotted"? (W.r.t. pulling on the ends.)
Bearing in mind that the ends may in general lie deep within the convex hull of the walk, perhaps this question requires rather more careful definition ... WFL
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