MATHEMATICS OF DNA STRUCTURE FUNCTION AND INTERACTIONS PDF
Mathematics of DNA structure, function and interactions. Selected papers based on the presentations at the workshop, September 16–21, , Minneapolis. Mathematics of DNA Structure, Function and Interactions PDF · Mathematical Methods in Dna Topology: Applications to Chromosome Organization and. Mathematics of DNA Structure, Function and Interactions Digitally watermarked , DRM-free; Included format: PDF; ebooks can be used on all reading devices.
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C.J. Benham et al. (eds.), Mathematics of DNA Structure, Function and Interactions,. The IMA Volumes in Mathematics and its Applications Laura Finzi. Differences between positively and negatively supercoiled DNA that topoisomerases may distinguish. Read and learn for free about the following article: DNA structure and function. that are fine-tuned to interact with this molecular structure in specific ways.
This complexity has arisen as living things have passed through the filter of natural selection.
If we look back to the beginnings of life, there must have existed a sort of porous wall in time before which there were only molecules subject to the laws of thermodynamics and mechanics but after which there were complex self-organizing, self-assembling, self-reproducing and self-adapting systems of molecules, now subject to evolution. Whatever may be the point or points in space and time at which this barrier was passed—however, and wherever life arose—it must have been passed at some point, and understanding the passage must be vital to arriving at a theoretical biology that may be called a theory of life.
Indeed, I would assert that the prime task of biology is to learn and understand this language so that we could then compute organisms from their DNA sequences. It is our view that it is this emergence of complex interacting elements that are acting ultimately under the laws of physics and chemistry that makes living matter different from the inanimate.
Mathematics of DNA Structure, Function and Interactions
However, the complexity attained depends on a system's history; on its evolution. While the involvement of the past of a system in its present can be found in some physical and chemical systems, in phenomena ranging from hysteresis on short time scales to geological pattern formation at long times, the significant difference in living matter is the accompanying growth of complexity it is worthy of note that biology shares this trait with technological and economic systems, as well as with culture and the arts.
We now have the human genome and we find Homo sapiens possesses some 23 genes [ 4 ]. A nematode worm, Caenorhabditis elegans, on the other hand, has 19 [ 5 ]. Are we really little more than worms?
It gets worse, some plants have enormous genomes: Paris japonica's is about billion base pairs long, some 50 times the human genome [ 6 ]. We can see two complementary answers to these riddles: the first is that the genome, the information used to construct a human or a worm, which is written in language we have yet to decode is clearly not a simple linear list of instructions, but a program, with subroutines, callbacks, loops and all the complexity that implies, so that one can talk of the further possible combinations of instructions—the additional combinatorial complexity—of our genome over the nematode's.
TOPOLOGY OF CIRCULAR DNA
Moreover, the genes represent only a small part of the genome, and the rest, including what has been injudiciously termed junk DNA, probably contains a great deal of information following our computing analogy, this may include variable and constant definitions and so on.
The second is that the genome only specifies what it must to get the job done, and so, if without further genetic intervention, a certain process will take place following the evolution of a physical or chemical system alone, then nature may take advantage of this; the genes act just as the choreographers.
Some processes are more tightly choreographed than others: we now know that segmentation in Drosophila is a process tightly genetically controlled by a number of genes, yet other similar processes have much looser control. See figure 1.
The biochemical puzzle of the genetic code was thus reduced to an abstract problem of symbol manipulation, as other physical scientists also saw, and for a few years physical scientists made large contributions to resolving the mysteries of genetics.
These efforts led to the sequencing of the whole human genome; the Human Genome Project triggered strong hopes, inter alia, of the possibility of diagnosing and treating many serious diseases. However, more than a decade after its completion in , it is generally acknowledged that these expectations have not been met.
A article by S. One such issue, the patterning of animal skins into stripes and spots, was the subject of a mathematical model created by the famous British mathematician Alan Turing.
As Ouellette reported, such morphogens have been found for zebra fish stripes, and behave pretty much as Turing predicted.
But what about the horse part? Our first problem explores the kind of issues that need to be solved by DNA programming to create 3-D structures.
DNA as information: at the crossroads between biology, mathematics, physics and chemistry
Note that this example is not based on an actual biological case but is meant to illustrate the general principles of how chemical gradients can be used by the embryo in conjunction with constraints in properties of available molecules.
Problem 1 In this problem you have to figure out the details of a hypothetical scenario in which a growing embryo can initiate the formation of two bony rods in the middle of its body using morphogens.
Imagine a rectangular sheet consisting of vertical columns and horizontal rows of identical round cells lined end to end. The cells along the left edge in column 0 can sense that they are on the edge, and can activate genes to release three different morphogens, A through C, in different concentrations. Each morphogen achieves its highest concentration at the left edge of the sheet, but each diffuses at different rates, so that the concentrations of A, B and C respectively at the right edge are 0.
Each cell in the sheet is programmed to make three pairs of molecules — one pair for each morphogen. These molecules get switched on or off based on the concentration of their particular morphogen as shown in the table below.
Topological Behavior of Plasmid DNA
The bone initiators and suppressors related to the other morphogens function similarly, but at different concentrations of their morphogens as shown below. Each bone suppressor, when active, completely blocks the action of its corresponding bone initiator.Helicases use chemical energy from ATP to disrupt the structure of double-stranded nucleic acid molecules. Here we primarily use mass action kinetic rates as attributes, but we could just as easily have used an emerging synthetic biology unit like polymerase per second PoPS  , .
Beausang, Philip C.
During transcription, the movement of RNA polymerase induces negative supercoiling upstream and positive supercoiling downstream the site of transcription. Each of the 6 windows is analogous to the previously described two-parameter bifurcation diagram for that pair of repressors .
Constructs near the edge of the cusp operate near saddle-node bifurcations and are more prone to noise-induced switching.
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