Re: [math-fun] J Borwein's sig
This AMS article talks exclusively about _circular_ DNA -- e.g., that found in some bacteria & in mitochondria. I believe that this is because bacteria/mitochondria have to use DNA itself to make stuff directly, rather than first translating into RNA. It may also have relevance to _RNA_, but this AMS paper doesn't talk about RNA. Once again, I'm not aware of any evidence that non-circular DNA is knotted. At 09:19 AM 12/25/2012, W. Edwin Clark wrote:
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
Bacteria do not synthesize protein from DNA, but from mRNA just as eukaryotes do. The same mechanisms are used (which is how they were discovered) with the exception of post-transcriptional splicing. Some bacteria have linear chromosomes, but most are circular. Topoisomerase plays a critical role in all bacteria. Many antibiotics target topoisomerase, and are lethal because they inhibit it. On Dec 25, 2012, at 1:16 PM, Henry Baker wrote:
This AMS article talks exclusively about _circular_ DNA -- e.g., that found in some bacteria & in mitochondria. I believe that this is because bacteria/mitochondria have to use DNA itself to make stuff directly, rather than first translating into RNA.
It may also have relevance to _RNA_, but this AMS paper doesn't talk about RNA.
Once again, I'm not aware of any evidence that non-circular DNA is knotted.
At 09:19 AM 12/25/2012, W. Edwin Clark wrote:
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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I looked over the Sumners article (see link below) again, and realized that he is talking primarily about _recombination_, a process in which DNA is purposely broken and reconnected again in different places and possibly different orders. I can well imagine that all sorts of things (both good and bad) can happen during this process, including the possibility of creating knots. I don't know what % of the time (human nuclear--i.e., non-mitochondrial) DNA spends doing recombination, but I would guess/hope very small. During the rest of the time, it is my understanding that there aren't any knots in this DNA. Thanks again to Edwin for the link to this interesting article. Conway must have previously talked about some of these ideas on math-fun years ago, because some of the ideas I was mentioning in another post seem to have come directly from Conway's "tangle theory", and I know that I've never read any of Conway's papers on tangle theory. At 07:32 AM 12/26/2012, Tom Knight wrote:
Bacteria do not synthesize protein from DNA, but from mRNA just as eukaryotes do. The same mechanisms are used (which is how they were discovered) with the exception of post-transcriptional splicing. Some bacteria have linear chromosomes, but most are circular. Topoisomerase plays a critical role in all bacteria. Many antibiotics target topoisomerase, and are lethal because they inhibit it.
On Dec 25, 2012, at 1:16 PM, Henry Baker wrote:
This AMS article talks exclusively about _circular_ DNA -- e.g., that found in some bacteria & in mitochondria. I believe that this is because bacteria/mitochondria have to use DNA itself to make stuff directly, rather than first translating into RNA.
It may also have relevance to _RNA_, but this AMS paper doesn't talk about RNA.
Once again, I'm not aware of any evidence that non-circular DNA is knotted.
At 09:19 AM 12/25/2012, W. Edwin Clark wrote:
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
On Fri, Dec 28, 2012 at 11:56 AM, Henry Baker <hbaker1@pipeline.com> wrote: I don't know what % of the time (human nuclear--i.e., non-mitochondrial)
DNA spends doing recombination, but I would guess/hope very small. During the rest of the time, it is my understanding that there aren't any knots in this DNA.
I'm sorry, I didn't realize we were still arguing about this question of fact. Let me re-post the link from up-thread, along with the beginning of the article this time. http://www.ncbi.nlm.nih.gov/pubmed/22187153 "Topo IV is the topoisomerase that knots and unknots sister duplexes during DNA replication" --------- Among the three classical DNA topological forms: supercoils, catenanes and knots, the former two are a direct consequence of fundamental DNA metabolic processes: transcription and replication (1). They were early recognized as soon as the model for the DNA double helix was originally proposed (2). DNA knots, on the other hand, although recognized even before (3), arise mainly as a by-product of topoisomerase II-mediated double-stranded passages (4). Knots in DNA have potentially devastating effects for cells (5,6) and therefore need to be quickly removed. DNA knots, however, form in vivo in non-replicating cells (7–9) and also during replication (10–14). It is important to distinguish, though, between unreplicated circular molecules with intramolecular knots and partially replicated molecules with intra- or interchromatid knots (Figure 1A and B). Although type-I DNA topoisomerases and DNA gyrase can knot and unknot DNA duplexes in vitro (15), it is firmly established that in vivo, Topo IV is the only topoisomerase significantly involved in decatenation and unknotting of DNA molecules (16–20). But how and why DNA becomes knotted in the first place is not entirely understood. Here, we show that Topo IV is also the topoisomerase that makes knots during DNA replication. This observation implies an unforeseen paradox, as the same enzyme that knots DNA is responsible for their removal later on, consuming ATP in both processes. --------- The article also includes AFM (atomic force microscopy) pictures of knotted E. coli DNA. --Michael
Thanks again to Edwin for the link to this interesting article. Conway must have previously talked about some of these ideas on math-fun years ago, because some of the ideas I was mentioning in another post seem to have come directly from Conway's "tangle theory", and I know that I've never read any of Conway's papers on tangle theory.
At 07:32 AM 12/26/2012, Tom Knight wrote:
Bacteria do not synthesize protein from DNA, but from mRNA just as eukaryotes do. The same mechanisms are used (which is how they were discovered) with the exception of post-transcriptional splicing. Some bacteria have linear chromosomes, but most are circular. Topoisomerase plays a critical role in all bacteria. Many antibiotics target topoisomerase, and are lethal because they inhibit it.
On Dec 25, 2012, at 1:16 PM, Henry Baker wrote:
This AMS article talks exclusively about _circular_ DNA -- e.g., that found in some bacteria & in mitochondria. I believe that this is because bacteria/mitochondria have to use DNA itself to make stuff directly, rather than first translating into RNA.
It may also have relevance to _RNA_, but this AMS paper doesn't talk about RNA.
Once again, I'm not aware of any evidence that non-circular DNA is knotted.
At 09:19 AM 12/25/2012, W. Edwin Clark wrote:
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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-- Forewarned is worth an octopus in the bush.
Just on topological grounds, this sounds to me more like linking than knotting. --Dan << Not [no knots] 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.
participants (4)
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Dan Asimov -
Henry Baker -
Michael Kleber -
Tom Knight