j. arsuaga- dna supercoiling
TRANSCRIPT
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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, math 195-3