|
|||||
Unknotting DNA
6th April 2018
|
HOME | ||||
"You should let the world know that the true source of mathematical methods as applicable to physics is to be found in the Proceedings of the Royal Society of Edinburgh. The volume- surface- and line- integrals of vectors and quaternions and their properties as in the course of being worked out by Tait is worth all that is going on in other seats of learning." - James Clerk Maxwell, 1871. |
In this blog we discuss the application of the knot theory in DNA structure. We will continue our discussions in Quantum Computing series afterwards. We had earlier described the importance of the measurement capacity of a macroscopic observer in j-space and how it results in an Unknot (Shallow Well) and Trefoil knot (Box). We next developed the description of a Trefoil knot in j-space. The description was in form of Laurent polynomials and it satisfied the following properties:
The knot diagram for the figure-8 knot, is shown as following: ![]() The knot polynomial for the figure-8 knot can be written, in the manner similar to the one introduced for Trefoil knot earlier as following: ![]() ![]() If we compare the Trefoil
and Figure-8 knots, we notice the absence of constant in the knot
polynomial for Figure-8 knot. The Trefoil knot in contrast has
for example, a value "3" representing the contributions of 0j. This is an important difference as the absence of the contribution of 0j
in the knot polynomial for figure-8 knot, represents
a corresponding physical structure, which has no memory of the
initial state.
The
structures with no memory of the initial state, are statistical in
nature described by the random variables. Thus if we write a knot
polynomial which shows no contribution of 0j,
then it is likely to be of statistical nature. Such structures
can be further reduced by a process similar to symmetry breaking, until
contribution of 0j
is accounted for, in the knot polynomials. The most fundamental
structure in j-space is represented by Trefoil knot, which has
three alternating crossings, the required minimum, to form a stable
knot.
A Comparison Criterion for DNA and Enzymes: A fantastic application will be to apply j-space knot polynomials, to the mechanism used by enzymes to unpack DNAs for replication. In j-space, enzymes and DNA both are observers, who are making measurements and being measured at the same time. Each molecule in a DNA represents a measurement. Subsequently by stringing together these measurements, a knot polynomial can be written for a specific DNA. The DNA represented by knot polynomials with no contribution from 0j term, are more likely to be affected by enzymes and hence easy to replicate. If the enzyme is related to a potentially catastrophic disease then such DNA are at risk. Similarly the DNA represented by very high contributions of 0j term in their knot polynomials, are likely to be much more robust. ![]() ![]() DNA and Enzymes Taking
the argument further we can possibly also write similar knot
polynomials for enzymes in j-space. If we compare the knot
polynomials written for enzymes and DNA, the enzymes corresponding to
the polynomials of lower order (t-n, t+n) and with high contributions of 0j terms, are more likely to succeed in breaking down DNA with higher order polynomials which have small contributions of 0j terms.
In similar fashion, the DNA with lower order polynomials and with high contributions from 0j terms, should be immune to the effects of enzymes corresponding to higher order polynomials and with little contributions from 0j terms. ***
![]() |
Previous Blogs: Chiral Symmetry
Sigma-z and I Spin Matrices Rationale behind Irrational Numbers The Ubiquitous z-Axis Majorana ZFC Axioms Set Theory Nutshell-2014 Knots in j-Space Supercolliders Force Riemann Hypothesis Andromeda Nebula Infinite Fulcrum Cauchy and Gaussian Distributions Discrete Space, b-Field & Lower Mass Bound Incompleteness II The Supersymmetry The Cat in Box The Initial State and Symmetries Incompleteness I Discrete Measurement Space The Frog in Well Visual Complex Analysis The Einstein Theory of Relativity *** |
|||
Information on www.ijspace.org is licensed under a Creative Commons Attribution 4.0 International License. Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits. This is a human-readable summary of (and not a substitute for) the license. |