The selfassembly of associating DNA molecules

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The self-assembly of associating DNA molecules in
flow Brownian dynamics simulation
Min Sun Yeom
Supercomputing Application Support
Team,  Supercomputing Center, KISTI
2006? 11? 20?(?)21?(?) ?????
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Self-assembly
from Wikipedia
is the fundamental principle which generates
structural organization on all scales from
molecules to galaxies. It is defined as
reversible processes in which pre-existing parts
or disordered components of a preexisting system
form structures of patterns. Self-assembly can be
classified as either static or dynamic. Static
self-assembly is when the ordered state occurs
when the system is in equilibrium and does not
dissipate energy. Dynamic self-assembly is when
the ordered state requires dissipation of energy
( weather patterns, solar systems and
self-assembled monolayers).

• Molecular self-assembly is the assembly of
  molecules without guidance or management from an
  outside source. There are two types of
  self-assembly, intramolecular self-assembly
  (secondary and tertiary structure protein
  folding) and intermolecular self-assembly
  (quarternary structure micelle )

3
Self-assembly
There are several reasons for interest in
self-assembly. First, humans are attracted by the
appearance of order from disorder. Second,
living cells self-assemble, and understanding
life will therefore require understanding
self-assembly. The cell also offers countless
examples of functional self-assembly that
stimulate the design of non-living systems.
Third, self-assembly is one of the few
practical strategies for making ensembles of
nanostructures. It will therefore be an essential
part of nanotechnology. Fourth, manufacturing
and robotics will benefit from applications of
self-assembly. Fifth, self-assembly is common
to many dynamic, multicomponent systems, from
smart materials and self-healing structures to
netted sensors and computer networks. Finally,
the focus on spontaneous development of patterns
bridges the study of distinct components and the
study of systems with many interacting components.
George M. Whitesides and Bartosz Grzybowski,
SCIENCE VOL 295 29 MARCH 2002
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Single Polymer Dynamics in flow
Douglas E. Smith and Steven Chu, SCIENCE VOL 281
28 AUGUST 1998 Thomas T. Perkins, Douglas E.
Smith, Steven Chu, SCIENCE VOL. 276 27 JUNE 1997
5
Shear-Induced Assembly of Lambda-Phage DNA

• ?-Phage DNA

• double-stranded helix
• 48502bp, 30.6MDa, 17.2

• termini
• 12-nucleotide-long, single-strand

Charbel Haber and Denis Wirtz, Biophysical
Journal Volume 79 September 2000 15301536
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The self-assembly of associating DNA molecules in
flow

• Mechanism difference (extensional shear
  flow)

• Simulation method model

• Properties

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• Brownian dynamics simulation

• Bead-spring model

• 1000 associating DNA molecules
• with 11 beads,10 springs

• Periodic boundary conditions

• Linked list method and Verlet neighbor list

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Brownian dynamics simulation

• Stochastic differential equation

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Model

• Force and potentials

• Worklike spring model

• Excluded volume potential

10

• Specific interaction

The value of C determines the strength of the
attraction
the unit vector between center of the end bead
and that of the adjacent linked bead
determines the position of the spot
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Properties parameters

• Radius of gyration

• Contour length

• Stretch

• Parameters

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• The probability distribution of fractional
  extension

• The distribution function of associating DNA end
  beads

• The distance between two beads

• Hydrodynamic interactions

• Periodic boundary conditions

- twice the range of the interaction potential
- shear,planar/uniaxial

• Comparision

- equivalent values of the second scalar
invariant of the strain rate tensor
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Results
Fig. 1. The radius of gyration of DNA molecules
at the formation time as a function of
Weissenberg number.
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Fig. 2. The contour length and stretch of DNA
molecules at the formation time as a function of
Weissenberg number.
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Fig. 3. The end to end distance of DNA molecules
at the formation time as a function of
Weissenberg number.
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Fig. 4. The elapsed time to form an initial
multimer (formation time) as a function of
Weissenberg number .
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Fig. 5. The probability distribution of
fractional extension in the flow direction at
the formation time for We 0,3,5,10 and 100
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Fig. 6. The probability distribution of
fractional extension in the flow direction as a
function of time at We 1000
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Fig. 7. The distribution function of DNA end
beads at the formation time as a function of
distance.
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Fig. 8. The average elapsed time to form an
initial multimer (formation time) as a function
of Weissenberg number.
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Fig. 9. The probability distribution of
fractional extension under extensional /shear
flow at the formation time for
various Weissenberg numbers.
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Fig. 10. The distance between two beads under
extensional /shaer flow as a function of time at
We 100.
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Fig. 11. The probability distribution of reduced
bond extension under extensional/shear flow as a
function of time at We 100.
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Fig. 12. The probability distribution of
fractional extension under extensional/shear flow
as a function of time at We 100.
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Fig. 13. The probability distribution of
fractional extension under extensional/shear
flow as a function of time at We 10.
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Fig. 14. The distribution function of associating
DNA end beads at the formation time as a
function of distance.
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Conclusions

• A shear and extensional flow deforms and
  stretches molecules and generates
• different distribution between end beads
  with sticky spot. The fractional
• extension progresses rapidly in shear flow
  from Gaussian-like distribution to
• uniform distribution. The progress of the
  distribution of fractional extension
• increases the possibility of meeting of end
  beads.

• In shear flow, the inducement of the assembly
  mainly results from the progress
• of the probability distribution of
  fractional extension. In extensional flow, the
• assembly is induced by both the progress of
  the probability distribution and
• increasing the values of the radial
  distribution.