A Coarse-Grained Model of DNA Nanotube Population Growth

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 behavior of nanotubes 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.

[1]  Erik Winfree,et al.  Integrating DNA strand-displacement circuitry with DNA tile self-assembly , 2013, Nature Communications.

[2]  Erik Winfree,et al.  Direct atomic force microscopy observation of DNA tile crystal growth at the single-molecule level. , 2012, Journal of the American Chemical Society.

[3]  Rebecca Schulman,et al.  Directing self-assembly of DNA nanotubes using programmable seeds. , 2013, Nano letters.

[4]  E. Winfree,et al.  Synthesis of crystals with a programmable kinetic barrier to nucleation , 2007, Proceedings of the National Academy of Sciences.

[5]  Hao Yan,et al.  Control of Self-Assembly of DNA Tubules Through Integration of Gold Nanoparticles , 2009, Science.

[6]  E. Winfree.  Simulations of Computing by Self-Assembly , 1998 .

[7]  S. Leibler,et al.  Kinetics of self-assembling microtubules: an "inverse problem" in biochemistry. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[8]  A. Turberfield,et al.  Self-assembly of chiral DNA nanotubes. , 2004, Journal of the American Chemical Society.

[9]  S. Andrews.  Methods for modeling cytoskeletal and DNA filaments , 2014, Physical biology.

[10]  Axel Ekani-Nkodo,et al.  Joining and scission in the self-assembly of nanotubes from DNA tiles. , 2004, Physical review letters.

[11]  Erik Winfree,et al.  Determining hydrodynamic forces in bursting bubbles using DNA nanotube mechanics , 2015, Proceedings of the National Academy of Sciences.

[12]  Shawn M. Douglas,et al.  DNA-nanotube-induced alignment of membrane proteins for NMR structure determination , 2007, Proceedings of the National Academy of Sciences.

[13]  Erik Winfree,et al.  Complexity of Self-Assembled Shapes , 2004, SIAM J. Comput..

[14]  Sudheer Sahu,et al.  Compact Error-Resilient Computational DNA Tilings , 2006, Nanotechnology: Science and Computation.

[15]  E. Winfree,et al.  Design and characterization of programmable DNA nanotubes. , 2004, Journal of the American Chemical Society.

[16]  J. Reif,et al.  DNA nanotubes self-assembled from triple-crossover tiles as templates for conductive nanowires. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[17]  Tuomas P. J. Knowles,et al.  An Analytical Solution to the Kinetics of Breakable Filament Assembly , 2009, Science.

[18]  H. S. Fogler,et al.  Elements of Chemical Reaction Engineering (4th Edition) (Prentice Hall International Series in the Physical and Chemical Engineering Sciences) (Hardcover) , 2005 .