Effects of DNA structure on its micromechanical properties

1
Effects of DNA structure on its micromechanical
properties

• Yuri Popov
• University of California, Santa Barbara
• Alexei Tkachenko
• University of Michigan, Ann Arbor
• June 2007

2
Mechanical properties of a single DNA molecule

• Single DNA stretching experiments Smith et al
  (1992)
• Marko and Siggia (1995)
• Elastic properties of a single DNA molecule are
  best described by the wormlike chain model, with
  bending energy

where persistence length lp 53 nm
3
Effects of sequence disorder on DNA looping and
cyclization

• Phys. Rev. E, in press
• arXivcond-mat/0510302

4
DNA looping

• Protein-mediated looping in regulation of gene
  expression (transcription control e.g. by lac
  repressor)
• DNA packaging into nucleosomes (wrapping around
  histones)
• Understanding spontaneous looping is a
  prerequisite to understanding protein-mediated one

5
Cyclization probability (J-factor)
DNA
looping
cyclization

• J-factor

6
Classical theory

• Theory (Shimada and Yamakawa, 1984)

7
Classical theory vs. experiment
cyclization

• Theory (Shimada and Yamakawa, 1984)
• Experiment (Cloutier and Widom, 2004)

For L 94 bp
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1. Effect of intrinsic curvature

• Effective energy of a chain with a random
  sequence
• Here k(s) is the intrinsic curvature for a
  random sequence it is Guassian with zero average

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1. Effect of intrinsic curvature

• Exact result for the ensemble-averaged J-factor
• with renormalized persistence length in the
  original result
• For consensus-scale data of Gabrielian,
  Vlahovicek, and Pongor (1998) k0lp 0.13

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1. Effect of intrinsic curvature
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2. Effect of random bending rigidity

• Effective energy of a chain with a random
  sequence
• J-factor for a particular sequence
  instead of

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2. Effect of random bending rigidity

• Effective energy of a chain with a random
  sequence
• J-factor for a particular sequence
  instead of

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Probability distribution of J
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2. Effect of random bending rigidity
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Overall effect of sequence disorder
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Summary

• Effect of sequence disorder is strong and always
  present. Sequence disorder gives rise to
  orders-of-magnitude variation in cyclization
  probability for completely random sequences
• Most importantly, there is no self-averaging in
  DNA looping or cyclization. The J-factor is not
  a well-defined function of the chain length L,
  not even to the first approximation. No
  typical DNA.
• Effects of random bending rigidity and intrinsic
  curvature provide comparable contribution
• Boundary conditions may be the key to explaining
  the experimental results

17
Effects of kinks on DNA elasticity

• Phys. Rev. E 71, 051905 (2005)
• arXivcond-mat/0410591

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Model

• Theoretical study of the effects of localized
  structural singularities on the elastic behavior
  of double- and single-stranded DNA
• Model wormlike chain with reversible kinks
• Want to know the elastic response (extension vs.
  force)

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What systems are described by this model?

• Protein-induced bending and looping in dsDNA
• Elastic description of ssDNA/RNA (trans-gauche
  rotations)
• Need a hybrid model where the finite bond
  elasticity is combined with structural defects
  (i.e. WLC with discrete features)

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Theoretical approach

• Chain is stretched by force F in the z direction
• Effective energy of a chain segment between two
  kinks
• Here t ?r/?s is tangent vector, si is location
  of kink i, L S(si1-si) is total
  length of the chain
• Constraint at each kink
• Here K is opening angle of each kink, ? is
  average line density of kinks without force

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Analogy with Quantum Rotator

• Schrodinger-like (diffusion) equation for
  evolution along the chain
• Here ?(t) is the chain propagator (distribution
  function of chain ends orientations) and H is the
  effective Hamiltonian
• The lowest eigenvalue determines the free energy

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Solution

• Analytical solve the eigenvalue problem by
  variational method with trial function
• where ? is variational parameter
• Numerical solve the original evolution problem
  directly

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Results K135
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Results K90
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Results K45
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Small stretching forces

• Elastic response is characterized by the
  renormalized persistence length
• Upon proper geometrical identification, exactly
  reproduces the Flory model for trans-gauche
  rotational isomers in the limit of high bending
  rigidity and rare kinks

27
Large stretching forces

• Main order pure wormlike chain result
• Exponential corrections due to the ideal gas of
  kinks

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Results K45
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Why the difference between numerical and
analytical results?

• Inadequate variational trial function ?(t) for
  smaller angles
• Secondary peak kink pairs
• Favorable little bending and short
  non-aligned portion

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Summary

• Hybrid model, with both the discrete defects and
  bending worm-like rigidity
• Small forces renormalized persistence length.
  Crossover between WLC and rotational isomer model
• Large forces WLC with the ideal gas of kinks
• High rigidity, small kink angle kink pairing

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THANK YOU
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References

• J. F. Marko and E. D. Siggia, Macromolecules, 28,
  8759 (1995)
• J. Shimada and H. Yamakawa, Macromolecules, 17,
  689 (1984)
• T. E. Cloutier and J. Widom, Molecular Cell, 14,
  355 (2004)
• A. Gabrielian, K. Vlahovicek, and S. Pongor, DNA
  tools, http//hydra.icgeb.trieste.it/kristian/dna
  /index.html
• M. G. Munteanu, K. Vlahovicek, S. Parthasarathy,
  I. Simon, and S. Pongor, TIBS, 23, 341 (1998)
• P. A. Wiggins, R. Phillips, and P. C. Nelson,
  arXivcond-mat/04092003