A coarse-grained model captures the temporal evolution of DNA nanotube length distributions

  • Vahid Mardanlou
  • Kimia C. Yaghoubi
  • Leopold N. Green
  • Hari K. K. Subramanian
  • Rizal F. Hariadi
  • Jongmin Kim
  • Elisa Franco
Article

Abstract

We derive a coarse-grained model that captures the temporal evolution of DNA nanotube length distribution during growth experiments. The model takes into account nucleation, polymerization, joining, and fragmentation processes in the nanotube population. The continuous length distribution is segmented, and the time evolution of the nanotube concentration in each length bin is modeled using ordinary differential equations. The binning choice determines the level of coarse graining. This model can handle time varying concentration of tiles, and we foresee that it will be useful to model dynamic behaviors in other types of biomolecular polymers.

Keywords

DNA nanotubes Ordinary differential equations Growth Dynamic DNA nanotechnology 

Notes

Acknowledgements

The authors thank Deborah K. Fygenson, Bernard Yurke, Rebecca Schulman, and Martha Grover for advice and discussions. This research was entirely supported by DE Grant SC0010595.

References

  1. Andrews SS (2014) Methods for modeling cytoskeletal and DNA filaments. Phys Biol 11(1):011,001CrossRefGoogle Scholar
  2. Douglas SM, Chou JJ, Shih WM (2007) DNA-nanotube-induced alignment of membrane proteins for NMR structure determination. Proc Natl Acad Sci 104(16):6644–6648CrossRefGoogle Scholar
  3. Ekani-Nkodo A, Kumar A, Fygenson DK (2004) Joining and scission in the self-assembly of nanotubes from DNA tiles. Phys Rev Lett 93(26):268,301CrossRefGoogle Scholar
  4. Evans CG, Hariadi RF, Winfree E (2012) Direct atomic force microscopy observation of DNA tile crystal growth at the single-molecule level. J Am Chem Soc 134(25):10485–10492CrossRefGoogle Scholar
  5. Flyvbjerg H, Jobs E, Leibler S (1996) Kinetics of self-assembling microtubules: an “inverse problem” in biochemistry. Proc Natl Acad Sci 93(12):5975–5979CrossRefMATHGoogle Scholar
  6. Fogler HS (2005) Elements of chemical reaction engineering, 4th edn. Prentice-Hall International, LondonGoogle Scholar
  7. Gillam J, MacPhee C (2013) Modelling amyloid fibril formation kinetics: mechanisms of nucleation and growth. J Phys Condens Matter 25(37):373,101CrossRefGoogle Scholar
  8. Gutenkunst RN, Waterfall JJ, Casey FP, Brown KS, Myers CR, Sethna JP (2007) Universally sloppy parameter sensitivities in systems biology models. PLoS Comput Biol 3(10):e189MathSciNetCrossRefGoogle Scholar
  9. Hariadi RF, Winfree E, Yurke B (2015) Determining hydrodynamic forces in bursting bubbles using DNA nanotube mechanics. Proc Natl Acad Sci 112(45):E6086–E6095CrossRefGoogle Scholar
  10. Hariadi RF, Yurke B, Winfree E (2015) Thermodynamics and kinetics of DNA nanotube polymerization from single-filament measurements. Chem Sci 6(4):2252–2267CrossRefGoogle Scholar
  11. Knowles TP, Waudby CA, Devlin GL, Cohen SI, Aguzzi A, Vendruscolo M, Terentjev EM, Welland ME, Dobson CM (2009) An analytical solution to the kinetics of breakable filament assembly. Science 326(5959):1533–1537CrossRefGoogle Scholar
  12. Liu D, Park SH, Reif JH, LaBean TH (2004) DNA nanotubes self-assembled from triple-crossover tiles as templates for conductive nanowires. Proc Natl Acad Sci USA 101(3):717–722CrossRefGoogle Scholar
  13. Mardanlou V, Green LN, Subramanian HK, Hariadi RF, Kim J, Franco E (2016) A coarse-grained model of DNA nanotube population growth. In: International conference on DNA-based computers. Springer, pp 135–147Google Scholar
  14. Markvoort AJ, Eikelder HMt, Hilbers PA, de Greef TF (2016) Fragmentation and coagulation in supramolecular (Co) polymerization kinetics. ACS Cent Sci 2(4):232–241CrossRefGoogle Scholar
  15. Mitchell JC, Harris JR, Malo J, Bath J, Turberfield AJ (2004) Self-assembly of chiral DNA nanotubes. J Am Chem Soc 126(50):16342–16343CrossRefGoogle Scholar
  16. Mohammed AM, Schulman R (2013) Directing self-assembly of DNA nanotubes using programmable seeds. Nano Lett 13(9):4006–4013CrossRefGoogle Scholar
  17. Reif JH, LaBean TH, Seeman NC (2000) Challenges and applications for self-assembled DNA nanostructures? In: International workshop on DNA-based computers. Springer, pp 173–198Google Scholar
  18. Reif JH, Sahu S, Yin P (2006) Compact error-resilient computational DNA tilings. In: Chen J, Jonoska N, Rozenberg G (eds) Nanotechnology: science and computation. Springer, pp 79–103Google Scholar
  19. Rothemund PWK, Ekani-Nkodo A, Papadakis N, Kumar A, Fygenson DK, Winfree E (2004) Design and characterization of programmable DNA nanotubes. J Am Chem Soc 126(50):16344–16352CrossRefGoogle Scholar
  20. Schulman R, Winfree E (2007) Synthesis of crystals with a programmable kinetic barrier to nucleation. Proc Natl Acad Sci 104(39):15236–15241CrossRefGoogle Scholar
  21. Sharma J, Chhabra R, Cheng A, Brownell J, Liu Y, Yan H (2009) Control of self-assembly of DNA tubules through integration of gold nanoparticles. Science 323(5910):112–116CrossRefGoogle Scholar
  22. Soloveichik D, Winfree E (2007) Complexity of self-assembled shapes. SIAM J Comput 36(6):1544–1569MathSciNetCrossRefMATHGoogle Scholar
  23. Subsoontorn P, Kim J, Winfree E (2012) Ensemble Bayesian analysis of bistability in a synthetic transcriptional switch. ACS Synth Biol 1(8):299–316CrossRefGoogle Scholar
  24. Winfree E (1998) Simulations of computing by self-assembly. Technical Report, California Institute of TechnologyGoogle Scholar
  25. Zhang DY, Hariadi RF, Choi HMT, Winfree E (2013) Integrating DNA strand-displacement circuitry with DNA tile self-assembly. Nat Commun 4:1965Google Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Electrical and Computer EngineeringUniversity of California at RiversideRiversideUSA
  2. 2.NeuroscienceUniversity of California at RiversideRiversideUSA
  3. 3.BioengineeringUniversity of California at RiversideRiversideUSA
  4. 4.Department of Physics and Biodesign InstituteArizona State UniversityTempeUSA
  5. 5.Wyss Institute for Biologically Inspired EngineeringHarvard UniversityBostonUSA
  6. 6.Mechanical EngineeringUniversity of California at RiversideRiversideUSA

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