The braiding of Life and the knotty DNA

 

YOU… You are just an untied knots of DNA which joined to form your physical body. In every cell of your body living or dead lies your code. The code of your bodily existence, and maybe also your initial mental construct. This code is highly compressed and tightly packed into the cell nucleus in the form of multiple linear DNA molecules forming a braided and knotted structures called chromosomes. A single human chromosome consists of DNA Molecule that is almost 5 cm on average and each human cell has approximately 2 m of DNA. Imagine packing this long thread in a volume of maybe less than, say, 10 μm. When the cell division begins, a second copy of its tangled up DNA is produced and this copy must be pulled apart without damaging  the original.There are certain Enzymes called topoisomerases (topo = a motif, iso= ,same) which assist this process of splitting and gluing the DNA strands by changing the DNA topology to facilitate functions such as replication or transcription. The magic is that these enzymes i.e. topoisomerases allow the molecules to pass through one another and separate!

Jones polynomial, are the mathematical objects used in modern molecular biology to study this phenomenon. In the mathematics, the Jones polynomial comes in the Knot theory and is named after its discoverer Vaughan Jones who presented this in 1984. This helps in distinguishing various knots which have different forms when expressed by this method. A circle traversed in clockwise direction has a monomial description and is expressed by just a number i.e. 1. In the interesting article by Davin Austin here, its shown how the links in the knots are undone using the Reidemeister moves, which are local in nature, demonstrated that two knot diagrams belonging to the same knot,  can be related by a sequence of the three moves as

  1. Twist and untwist in either direction i.e. turning.
  2. Move one loop completely over another i.e. slipping.
  3. Move a string completely over or under a crossing .i.e. poking.

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Reidemeister moves help in defining the knot invariants (properties of knots that do not change under these operations).  One such invariant is the Jones polynomial and another is the linking number (# of times that each curve winds around the other) that describes the linking of two closed curves in 3D space. The linking number is always an integer, but may be positive or negative depending on the orientation of the two curves.

This brings us to the DNA super-coiling, which helps compacting the DNA, and by regulating access to your life code. Here, the mathematical ideas introduced above play a vital role in  describing the supercoiling by comparing different coiled states with the standard B-DNA topology. For large chromosomes, the process proceeds by “anchoring” both the ends and the middle segments undergo the moves of untangling the DNA and as a result, they may be unable to distribute or absorb the twisting stress to the rest of the chromosome or recover from underwinding—the segments may become supercoiled, in other words. In response to supercoiling, they will assume an amount of writhe (the amount by which a segment of DNA is deformed as a result of this torsional stress) just as if their ends were joined. This process is considered to play a role in gene expression as well.

So, at the basis of everything we see around us seems to be hidden in mathematics. There are certain rules to this game of life and maybe this universe is full of intelligence at all levels. From the interplay of subatomic particles to the symphony of stars, everything seems to be coded in numbers. The strangest thing is the same universe that generated us, is studying itself through the sentient beings (as far as we know there is no other intelligent life) called homo sapiens, who are living on this blue planet Earth for over several millennia. Since the last two centuries, the industrial revolution at the outset and the information revolution at the fag end of twentieth century ushered an era of explosive research and huge amount of data which is accessible now for inspection and learning. Maybe some day we will be able to quantify those things as well; which to the present day seem unlikely candidates, e.g. Love. Who knows, if enlightenment is just a phase shift in human consciousness and one day we might know an equation that describes such a state or maybe not.

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