Research ArticleCHEMICAL PHYSICS

In silico construction of a flexibility-based DNA Brownian ratchet for directional nanoparticle delivery

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Science Advances  05 Apr 2019:
Vol. 5, no. 4, eaav4943
DOI: 10.1126/sciadv.aav4943
  • Fig. 1 A DNA fragment with flexibility gradient.

    (A) Model of dsDNA represented by a semiflexible chain of monomers, each of which models a group of 6 DNA base pairs. A dsDNA fragment with flexibility gradient is modeled by a chain of 64 monomers. The local persistence length (lp) is set for each monomer at either 51 or 40 nm. The sequence-dependent dsDNA flexibility is gradually increased by increasing the fraction of monomers with lp = 40 nm. (B) Bending energy of dsDNA fragment when it binds with a positively charged NP at solution salt concentrations of Con = 0.15 M and Coff = 0.81 M. The bending energy is calculated for a specific, representative conformation of the DNA-NP complex as shown in the inset of each figure along the flexibility gradient of 64-mer dsDNA presented in (A). The monomer number in the x axis represents the identity of the first DNA monomer bound to the NP.

  • Fig. 2 Construction of a DNA-based Brownian ratchet.

    (A and B) Long dsDNA containing four repeat fragments with the flexibility gradient, together with its DNA-NP binding potential energy along the entire dsDNA molecule at solution salt concentrations of Con = 0.15 M and Coff = 0.81M, respectively. (C) Solution salt concentrations are changed repeatedly between Con = 0.15 M and Coff = 0.81 M to turn the asymmetric DNA-NP binding potential on and off with a time period of τon and τoff.

  • Fig. 3 Directional rolling of an NP on a dsDNA fragment with flexibility gradient.

    Probability of the final location of an NP on a dsDNA fragment with flexibility gradient at Con = 0.15 M after BD simulations for a duration of τon = 104τBD, obtained from 200 independent simulations. The monomer number in the x axis represents the identity of the DNA monomer in the middle among those wrapping around an NP at a salt concentration of 0.15 M. Initial location of an NP was random on a dsDNA fragment at the beginning of the 200 simulations.

  • Fig. 4 Brownian motion of an NP at Coff = 0.81 M.

    (A) Probability of final location of an NP initially bound to the 60th monomer (most flexible region of the first repeat fragment) after each simulation duration of τoff = 5 × 102τBD, 103τBD, and 5 × 103τBD, calculated with a bin size of 16. (B) Probability of NP jump from the original repeat fragment to the other repeat fragments, ΔNjump, after τoff. ΔNjump is positive for forward direction and negative for backward direction. Light orange–colored shades indicate the original repeat fragment. These histogram data in the figures were obtained from 300 independent simulations at each τoff. (C) Probability of net directional motion of an NP in the forward direction (PfPb) estimated by the difference between probabilities for forward (Pf) and backward (Pb) diffusion of an NP after τoff.

  • Fig. 5 Simulation results of directional motion of an NP in the forward direction.

    (A) Net displacement of an NP with time starting from an original repeat fragment and arriving at a repeat fragment separated by ΔNjump fragments, presented for all 20 independent simulation sets with 40 repeated changes between salt concentrations of Con and Coff with simulation durations of τon = 104τBD and τoff = 103τBD. (B) Net displacement averaged over the 20 independent simulation sets for different simulation durations of τoff = 5 × 102τBD, 103τBD, 5 × 103τBD, and 104τBD. In each simulation set, the asymmetric potential is turned on and off repeatedly 20 times for τoff = 5 × 103τBD and 104τBD and 40 times for τoff = 5 × 102τBD and 103τBD. Positive values for ΔNjump indicates net displacement in the forward direction.

  • Fig. 6 DNA-NP under constant force field.

    (A) Snapshots of an NP with DNA at Con = 0.15 M subject to external forces, Fd, of 0.04, 0.20, and 0.40 pN. (B) Probability of final location of an NP at Coff = 0.81 M after BD simulations of τoff = 103τBD under external forces Fd = 0. 04 and 0.20 pN. An NP is initially bound to the most flexible region of a flexibility gradient, and this initial location is set to the monomer number of zero in the figures. The probability distributions in (B) are obtained from 180 independent simulations.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/4/eaav4943/DC1

    Fig. S1. Simulation model systems of DNA-NP binding at Con = 0.15 M under external force.

    Fig. S2. Probability distribution of an NP at Coff = 0.81 M after Brownian motion for a duration of τoff = 103τBD under external force.

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Simulation model systems of DNA-NP binding at Con = 0.15 M under external force.
    • Fig. S2. Probability distribution of an NP at Coff = 0.81 M after Brownian motion for a duration of τoff = 103τBD under external force.

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