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Monte Carlo study of DNA condensation phenomena

Monte Carlo study of DNA condensation phenomena. Russell Hanson Biology Graduate Student Association Symposium Oct 1, 2004. Outline. Overview Poisson-Boltzmann equation Metropolis Monte Carlo Theoretical models: DNA condensation Experimental and theoretical results

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Monte Carlo study of DNA condensation phenomena

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  1. Monte Carlo study of DNA condensation phenomena Russell Hanson Biology Graduate Student Association Symposium Oct 1, 2004

  2. Outline • Overview • Poisson-Boltzmann equation • Metropolis Monte Carlo • Theoretical models: DNA condensation • Experimental and theoretical results • Conclusions and future directions BGSA Symposium Oct 1, 2004

  3. Origin of Poisson-Boltzmann equation Poisson equation Gauss’ law combine… BGSA Symposium Oct 1, 2004

  4. Boltzmann distribution law For positively and negatively charged ions the work functions are: Let ionic strengths, i.e. number of positive and negative ions, be equal M+=M-. +ec is a charge. BGSA Symposium Oct 1, 2004

  5. Poisson-Boltzmann equation BGSA Symposium Oct 1, 2004

  6. Metropolis scheme Trial move Calculate energy deltaE = Enew - Eold if Enew < Eold move else Enew > Eold if random variable[0:1] < exp(-deltaE/kT) move else reject move BGSA Symposium Oct 1, 2004

  7. Monte Carlo example using Metropolis condition for 1D Ising system: average energy increasesas temperature increases BGSA Symposium Oct 1, 2004

  8. Theoretical models • Mean field approach (Poisson-Boltzmann and Debye-Hückel) • Explicit ions (Lyubartsev) • Hydration (Rau and Parsegian) • Cylindrical models: • line charge, helical, cylinder with major and minor grooves, helicity involved in observed attraction BGSA Symposium Oct 1, 2004

  9. Error in PB greater than 1% in close-packing region PM := Primitive model of DNA in cylindrical shell (Lyubartsev et al., 1995) (Petrov, 2004) BGSA Symposium Oct 1, 2004

  10. Trigonal and hexagonal cylindrical packing Trigonal packing (Lyubartsev et al., 1995) BGSA Symposium Oct 1, 2004

  11. Theoretical and experimental results (Lyubartsev et al., 1995) BGSA Symposium Oct 1, 2004 (Rau & Parsegian, 1992)

  12. Theoretical and experimental results (p2) Energy landscapes for interaction between two crossed B-DNA-like helices. Plotted interaxial angle ψ and difference in about-axis rotation angles φ2-φ1. (Kornyshev et al., 2000) BGSA Symposium Oct 1, 2004

  13. Conclusions and future directions • Force field improvement for DNA condensation in presence of ions • Polymer physics of viral capsid DNA folding • Future modeling (LaMarque et al., 2003) BGSA Symposium Oct 1, 2004

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