Re: [math-fun] J Borwein's sig
DNA does get incredibly _folded_ & kinked, but not mathematically _knotted_, at least according to the lectures I've listened to. There are some wonderful videos of DNA being replicated by a graphics group in Australia, which show how the two different strands are separated, one of them is broken up into chunks (because it has to be copied the other direction) and then copied & put together. If you believe these videos, there aren't any knots involved. At 07:45 AM 12/25/2012, Michael Kleber wrote:
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
It turns out to be very difficult to know the topological structure of DNA inside living cells -- everyone has assumed that DNA knots appeared in vivo for as long as we've known about any topoisomerase (since the 1980s!), and there have been many other pieces of evidence which point towards knots arising during regular biological processes since then. But I think direct imaging of knots in live cells is relatively recent. Maybe-interesting articles: http://www.ncbi.nlm.nih.gov/pubmed/22187153 http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2853108/ --Michael On Tue, Dec 25, 2012 at 11:10 AM, Henry Baker <hbaker1@pipeline.com> wrote:
DNA does get incredibly _folded_ & kinked, but not mathematically _knotted_, at least according to the lectures I've listened to.
There are some wonderful videos of DNA being replicated by a graphics group in Australia, which show how the two different strands are separated, one of them is broken up into chunks (because it has to be copied the other direction) and then copied & put together.
If you believe these videos, there aren't any knots involved.
At 07:45 AM 12/25/2012, Michael Kleber wrote:
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
-- Forewarned is worth an octopus in the bush.
You will find pictures of knots and links of DNA in this 1995 Notices of AMS article by DeWitt Summers one of the first knot theorist to look at DNA http://www.ams.org/notices/199505/sumners.pdf On Tue, Dec 25, 2012 at 11:10 AM, Henry Baker <hbaker1@pipeline.com> wrote:
DNA does get incredibly _folded_ & kinked, but not mathematically _knotted_, at least according to the lectures I've listened to.
There are some wonderful videos of DNA being replicated by a graphics group in Australia, which show how the two different strands are separated, one of them is broken up into chunks (because it has to be copied the other direction) and then copied & put together.
If you believe these videos, there aren't any knots involved.
At 07:45 AM 12/25/2012, Michael Kleber wrote:
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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W. Edwin Clark