J. Arsuaga- DNA Supercoiling

8/3/2019 J. Arsuaga- DNA Supercoiling

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March 16, 2010Math 414-1 / 714-1 Lecture 13

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3.2 DNA in nature is found in circular form

(plasmids) or as structures topologicallyequivalent to circles

Bates and Maxwel, DNA topology, 2005

Oxford University Press


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3.3. Supercoiling naturally appears in

many biological processes such as DNAreplication

Bates and Maxwel, DNA topology, 2005

Oxford University Press


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Supercoiling is observed in

chromosomes and is essential for cellviability


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Biological roles of supercoiling

DNA compaction

Helps the opening of the double helix during

DNA replication and transcription

Site-specific recombination


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Supercoiling is a wellness sensor for the

cell


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Supercoiling has broad implications in

replication & transcription

Replicated

domain

Replicating

domain

Pre-

replicated

domain


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Who takes care of Supercoiling in the

cell? Enzymes; type I andtype II topoisomerases

Figure courtesy of J. Roca


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Supercoiling in agarose gels


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3.4 How can we quantify supercoiling?


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How can we quantify supercoiling?

Intuitively: Supercoiling happens due to anexcess of the number of times that the two

DNA backbones coil around each other.

Note to the students: the following slides

are vague and should be complemented

with your lecture notes


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Consider a linear fragment of DNA:N=Number of base-pairs of thefragment

h=Number of base pairs/helical turnLk0=N/h~ #helical turn

Consider a planar circular molecule :Lkm= Closest integer to N/h

J. Arsuaga, math 195-3


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How can we compute the linking number

of any DNA molecule?General definition of Linking Number


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+1

+1

+1

-1


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+1

+1

+1

-1

Lk=1/2( sign(ci))

c1

c2


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Supercoiling

Linking number difference:Lk=Lk- Lk

0

Why Lk0 instead of Lkm?



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Supercoiling density: = Lk/ Lk0

Example:

In E. coli = -0.06



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Geometrical parameters Twist: Measures the coiling of the two

individual strands.

Tw0=N/h for open circular notnecessarily planar due to intrinsic curvature.

Writhe: Describes how the helix axis coilsin space.

Wr0=due to intrinsic curvature



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Calugareanu-White-Fuller Theorem

Lk=Tw+Wr



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Computer simulations of DNA

supercoiling: MD and Monte-Carlo

[Jian et al., 1998; Huang et al., 2001]



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Supercoiling is a wellness sensor for the

cell


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Chapter IV: The mathematics of DNA

supercoiling

Experimental evidence forsupercoiling and basicdefinitions.

Linking number, twist andwrithe

Whites theorem Modern experimental

techniques to studysupercoiling andapplications


J. Arsuaga- DNA Supercoiling

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