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Fractal properties of DNA.

Smrek, Jan.

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Fractal properties of DNA.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Fractal properties of DNA./
Author:	Smrek, Jan.
Description:	260 p.
Notes:	Source: Dissertation Abstracts International, Volume: 76-08(E), Section: B.
Contained By:	Dissertation Abstracts International76-08B(E).
Subject:	Polymer chemistry. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3685914
ISBN:	9781321624748

Fractal properties of DNA.
Smrek, Jan.

Fractal properties of DNA. - 260 p.

Source: Dissertation Abstracts International, Volume: 76-08(E), Section: B.

Thesis (Ph.D.)--New York University, 2015.

This item is not available from ProQuest Dissertations & Theses.

In this work we explore conformational and dynamical properties of eukaryotic interphase DNA from polymer physics perspective. We begin with an introduction to genome structure and review factors influencing the genome folding with the focus on high density and topology of the DNA chains. The natural tendency of long polymers to tangle competes with the simple topology, important for the biological functionality of the genome. The simple topology plays a central role in our discussion hence we estimate the relevant polymer parameters of the DNA, such as the entanglement length. We propose new theoretical arguments and review experimental evidence for, and against the hypothesis that the generic polymeric properties of topological constraints are a decisive factor in a specific self-similar (fractal) structure of the DNA conformation. As the simplest polymer model exhibiting the competition between high density and simple topology we discuss the melt of unknotted and unconcatenated polymer rings. We show how the simple topology of the melt of rings is reflected in microscopic structure and macroscopic properties that dramatically differ from highly tangled polymeric systems. We demonstrate how looking at the DNA and melt of rings systems in parallel can help to increase our understanding of both. It turns out, that the conformation of a ring in the melt, and that of the DNA in the nucleus share self-similar features reflected in the compact scaling of the gyration radius and power-law character of the contact probability.

ISBN: 9781321624748Subjects--Topical Terms:

3173488
Polymer chemistry.

Fractal properties of DNA.
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020 $a 9781321624748
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100 1 $a Smrek, Jan. $3 3192902
245 1 0 $a Fractal properties of DNA.
300 $a 260 p.
500 $a Source: Dissertation Abstracts International, Volume: 76-08(E), Section: B.
500 $a Adviser: Alexander Y. Grosberg.
502 $a Thesis (Ph.D.)--New York University, 2015.
506 $a This item is not available from ProQuest Dissertations & Theses.
520 $a In this work we explore conformational and dynamical properties of eukaryotic interphase DNA from polymer physics perspective. We begin with an introduction to genome structure and review factors influencing the genome folding with the focus on high density and topology of the DNA chains. The natural tendency of long polymers to tangle competes with the simple topology, important for the biological functionality of the genome. The simple topology plays a central role in our discussion hence we estimate the relevant polymer parameters of the DNA, such as the entanglement length. We propose new theoretical arguments and review experimental evidence for, and against the hypothesis that the generic polymeric properties of topological constraints are a decisive factor in a specific self-similar (fractal) structure of the DNA conformation. As the simplest polymer model exhibiting the competition between high density and simple topology we discuss the melt of unknotted and unconcatenated polymer rings. We show how the simple topology of the melt of rings is reflected in microscopic structure and macroscopic properties that dramatically differ from highly tangled polymeric systems. We demonstrate how looking at the DNA and melt of rings systems in parallel can help to increase our understanding of both. It turns out, that the conformation of a ring in the melt, and that of the DNA in the nucleus share self-similar features reflected in the compact scaling of the gyration radius and power-law character of the contact probability.
520 $a We show how thes specific fractal features can be manifested in a mathematical model of a novel class of space-filling curves representing the DNA polymer fiber. The compact gyration radius of the DNA is reflected in the fractal dimension of the curves being the one of the embedding space d, while the contact probability scaling is reproduced by the fractal dimension of the curve boundary to be close to d from below. The mathematical model allows us to address the entropic properties of such space-filling unknotted self-similar conformations, which would make a clear link between the topology and conformation. The derivation of the entropically favorable contact probability for a topologically simple yet self-similar curves seems a difficult problem, but we make a first step in this direction by directly enumerating Hilbert-like curves as the simplest representatives of the crumpled space-filling trajectories similar to DNA conformation.
520 $a Having a mathematical model that mimics the DNA conformation we investigate how does the conformation affect essential biological process such as diffusional search of proteins for their binding sites on the DNA. Besides specific binding to the target, the proteins bind also non-specifically and diffuse along the DNA fibers. Using scaling arguments and simulations of diffusion in the fractal medium of the space-filling curves, we show how does the protein target binding rate depend on the protein affinity for DNA and the fractal structure of the DNA conformation.
520 $a To examine in more detail the structure and the dynamics of topologically constrained polymers, we switch to the melt of unconcatenated rings. Motivated by a large-scale simulations of polymer tree-like conformations, that shared many conformational features with that of the rings in the melt, it was hypothesized that the rings have the structure of annealed branched trees. However an algorithm to find such structure was missing. Based on this structural hypothesis, we derive dynamical properties of the rings in the melt, postponing supportive evidence on the validity of the conjecture. Very good agreement with simulations and experiment is found for relaxation time, diffusion coefficient, relaxation modulus, viscosity and mean square displacements. This is somewhat surprising as the ring conformations in the molecular dynamics simulations are not rigid objects, but highly penetrate neighbors territories and indeed, by inspection, do not resemble doubly-folded trees. We briefly discuss relation of the ring dynamic properties to to those of the DNA.
520 $a To close the circle we span minimal surfaces on the ring conformations from the melt and find a linear scaling with ring length in support of the tree structure conjecture. Moreover, this approach enabled us to systematically quantify the ring threadings by means of ring penetration of neighboring ring's surface. We found that the threading is limited to lengths below five entanglement lengths and does not form a dense network to substantially hinder the relaxation. Besides the interesting results for the melt of rings, we spanned minimal surfaces also on freely fluctuating rings and obtained a new critical exponent of area scaling with ring length.
590 $a School code: 0146.
650 4 $a Polymer chemistry. $3 3173488
650 4 $a Biophysics. $3 518360
690 $a 0495
690 $a 0786
710 2 $a New York University. $b Physics. $3 3180022
773 0 $t Dissertation Abstracts International $g 76-08B(E).
790 $a 0146
791 $a Ph.D.
792 $a 2015
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3685914