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15 August 2004 | Draft

DNA Supercoiling as a Pattern for Understanding Psycho-social Twistedness

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This is an annex to Engaging with Questions of Higher Order: cognitive vigilance required for higher degrees of twistedness (2004)

Introduction
Structure of DNA
Forms of DNA
-- Supercoiled (or "knotted")
-- Relaxed
Descriptive properties associated with supercoiling
-- Writhing
-- Twisting
-- Linking number
-- Density
-- Replication
-- Denaturation, melting, breathing and unzipping
-- DNA-knots
Energy associated with different structures
-- Minimum energy (stable)
-- Higher energy (unstable)
References


Introduction

The review here of twistedness in DNA provides a technical basis for the discussion in the main paper (Engaging with Questions of Higher Order: cognitive vigilance required for higher degrees of twistedness, 2004).

The insights in the main paper regarding "twistedness" reflect an intuitive understanding of complexity which calls for deeper insight to understand how twistedness works and why it may be vitally important in some psycho-social processes -- as well as being highly problematic in others. Part of the difficulty in approaching this matter is that "twistedness" is in most cases used unthinkingly as a pejorative term to characterize a pattern which is felt to inhibit right-thinking and clarity. The argument here is that, given its importance at every scale in nature, from the organization of nebula to the organization of the human cell, there is a case for distinguishing various forms of twistedness and understanding their function. This could be especially valuable to reconciling apparently irreconcilable understandings in society.

The merit of focusing on the nature and function of twisting in DNA is that it provides a rich natural template. It offers a sense of the degree of complexity that it may be required to master in order to comprehend how twistedness "works" in practice. It might also be argued that, as a process active in every human body and inherent to human life, humans may well have some kind of profound intuitive understanding of how it works and the "rightness" of such working. Some of the very explicit dynamics of this process may also offer patterns for understanding how the inhibiting effects of "twistedness" may be addressed when they are perceived to be a constraint on human development.

Understanding of how DNA works has been much enriched by concepts from topology -- as a branch of mathematics that deals with structural properties that are unchanged by deformations such as stretching and bending. This use of mathematics is especially important because there is no experimental way to observe the dynamics of enzymatic action directly, notably with respect to knotting and coiling of DNA (see De Witt Sumners. Lifting the Curtain: Using Topology to Probe the Hidden Action of Enzymes, 1995; Xiaoyan R. Bao, et al. Behavior of Complex Knots in Single DNA Molecules, 2003).

Chromosomal DNA molecules are very long and thin. There is over a metre of DNA in every human cell in a space of some 0.0006 centimetres diametre. If DNA were constrained to be linear it would not fit into a cell. It must therefore fold many times to fit within the confines of a cell. The DNA is composed of 10** base pairs. This density of packing results in tangles and knots in the DNA that are essential to enable the cell to divide (involving transcription and replication).

Structure of DNA

DNA is a double stranded molecule composed of two polarized strands (of deoxyribonucleotide polymers) which run in opposite directions (termed antiparallel) and wind around a central, common axis -- one is entwined about the other such that an overall helical shape results (known as a plectonemic helix). Both are wound in a right-handed manner. This structure is to be contrasted with a paranemic helix, in which a pair of coils lie side by side without interwinding. The strands are occasionally distinguished as the Watson strand and the Crick strand.

In the case of the molecular structure of eukaryotic chromosomes in each human cel, 2 meztres of DNA is packaged into the cell nucleus. To access the information, it must be unwound as a double helix and needs to be "spread out" in the nucleus. However during cell division (mitosis), in order to move them around, they are packaged as follows into dense bundles:

Each nucleotide base of one strand is paired with a nucleotide base on the other strand to create a stable structure of the two polymers. The pairing of the four types of bases (A, T, C, G) by hydrogen bonds is not random: an A pairs with a T and a G pairs with a C. The bases on the outside of the helix are exposed to solvent within two grooves along the helix, the "major groove" and the "minor groove". It is within these grooves that DNA interacts with other molecules. The three structural variation of these grooves ("A", "B" and "Z" DNA), which differ in the relationship between the bases and the helical axis, offer one mechanism by which reactivity of DNA is modulated:

In circular double helix DNA (closed circular ccDNA), both strands are covalently joined to form a circular duplex molecule. The geometry of such an assembly is such that its number of coils cannot be changed without first breaking one of its strands. This topological "dilemma" is resolved within the cell -- to ensure proper biological functioning -- by specialized enzymes that unknot, untwist and unwind the DNA to enable replication and then reform the compact mode thereafter.

Heptad repeats: The coiled coil is a ubiquitous protein-folding motif. The accepted hallmark of the coiled coil is the seven-residue heptad repeat..A coiled-coil protein consists of two identical strands of amino acid sequences that wrap around each other. The amino acids in a coiled-coil structure reside on seven different structural positions on the coil, forming a heptad repeat (see The Heptad Repeat of The Coiled-coil Structure). Heptad repeats are characteristic of certain proteins. (see also images of David Gossard. Coiled Coils. 2003). Most coiled-coil sequences contain heptad repeats, namely seven residue patterns -- denoted abcdefg -- in which the a and d residues (core positions) are generally hydrophobic. As there are 3.6 residues to each turn of the alpha-helix, these a and d residues form a hydrophobic seam, which, as each heptad is slightly under two turns, slowly twists around the helix. The coiled-coil is formed by component helices coming together to bury their hydrophobic seams. As the hydrophobic seams twist around each helix, so the helices also twist to coil around each other, burying the hydrophobic seams and forming a supercoil. It is the characteristic interdigitation of side chains between neighbouring helices, known as knobs-into-holes packing, that defines the structure as a coiled coil (see Jenny Shipway. An Introduction to Coiled Coils. 2000) [more | more].

Forms of DNA

Supercoiling is thus vital to two major functions. It helps pack large circular rings of DNA into a small space by making the rings highly compact. It also helps in the unwinding of DNA required for its replication and transcription. Supercoiled DNA is thus the biological active form. The normal biological functioning of DNA occurs only if it is in the proper topological state.

Descriptive properties associated with supercoiling

"Supercoiling" is an abstract mathematical property, and represents the sum of what are termed "twist" and "writhe". "Supercoil" is seldom used as a noun with reference to DNA topology. It is the combination of twists and writhes that impart the supercoiling, and these occur in response to a change in the linking number. A coiled structure is at a higher energy (less stable). When the linking number is reduced in closed circular DNA, the molecule supercoils by minimizing twisting and bending. To partially relieve the strain introduced by the change in linking number (a 'deficit' in the link), the DNA must distort in other ways -- compensating with a change in twist or writhe. These are, physically, the two ways that the DNA can do so. The relationship of twist, writhe and supercoiling is expressed by the equation S = T + W (known as White's formula). Twist and writhe are geometric quantities. Unusually, link as a topological property is equal to the sum of two geometric properties. Their values change if the ribbon is deformed in space. Link, twist and writhe can be either positive or negative. Link is always an integer, whereas twist and writhe can take any real values.

Energy associated with different structures

The energy of the molecule changes if there is a change in pitch (that is, the number of bases per full turn) or bending of the double helix ring. Even a small change in the pitch of the DNA results in a large increase in energy


References

Ralf Metzler and Andreas Hanke. Knots, bubbles, untying, and breathing: probing the topology of DNA and other biomolecules. 2004 [text]

Jeremy Narby. The Cosmic Serpent: DNA and the Origins of Knowledge. New York, Jeremy P. Tarcher/Putnam, 1999

Daniele Focosi. Cell Cycles [text]

Rensselaer Polytechnic Institute. DNA Structure and Topology. [text]

N Patrick Higgins. Chromosome Structure .[text]

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