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

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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.

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Notes

  1. A bin size smaller than 0.3  \({\upmu }\)m is not advisable in our case due to the limited resolution of our microscope, which is roughly 0.1  \({\upmu }\)m per pixel. A length difference around 1 or 2 pixels is too uncertain to be trusted. (For this reason, nanotubes shorter than 0.3  \({\upmu }\)m were discarded in our image processing script.) This means that \(l_b=\)0.3  \({\upmu }\)m is the minimum bin size we can choose.

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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.

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Authors and Affiliations

  1. Electrical and Computer Engineering, University of California at Riverside, Riverside, CA, 92521, USA

    Vahid Mardanlou

  2. Neuroscience, University of California at Riverside, Riverside, CA, 92521, USA

    Kimia C. Yaghoubi

  3. Bioengineering, University of California at Riverside, Riverside, CA, 92521, USA

    Leopold N. Green

  4. Department of Physics and Biodesign Institute, Arizona State University, Tempe, AZ, 85287, USA

    Rizal F. Hariadi

  5. Wyss Institute for Biologically Inspired Engineering, Harvard University, Boston, MA, 02115, USA

    Jongmin Kim

  6. Mechanical Engineering, University of California at Riverside, Riverside, CA, 92521, USA

    Hari K. K. Subramanian & Elisa Franco

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  1. Vahid Mardanlou
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  2. Kimia C. Yaghoubi
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  3. Leopold N. Green
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  4. Hari K. K. Subramanian
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  5. Rizal F. Hariadi
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  6. Jongmin Kim
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  7. Elisa Franco
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Corresponding author

Correspondence to Elisa Franco.

Appendix

Appendix

Table  2 reports the best performing parameter set when the model is modified to have a bin size \(l_b=0.6\, {\upmu }\hbox {m}\) (we are increasing the model coarse-grainedness). Figure  8 shows an overview of the model performance (training and validation).

Table 2 Best fitted parameters for bin size of \(0.6\, {\upmu }\hbox {m}\)
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Fig. 8
figure 8

Overview of model fitting and validation when the nanotube length distribution bin size is \(l_b=0.6\, {\upmu }\hbox {m}\), twice the nominal \(l_b\) adopted in this paper. For brevity we do not show individual fits and predictions of nanotube cumulative distributions, histograms, and tile/nuclei concentrations over time; these plots look qualitatively similar to those in Figs.  3,  4, and  5. a Mean nanotube length. b Predicted and measured nanotube density (number of nanotubes in a \(100 \times 100\, {\upmu }\hbox {m}\) area). (Color figure online)

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Mardanlou, V., Yaghoubi, K.C., Green, L.N. et al. A coarse-grained model captures the temporal evolution of DNA nanotube length distributions. Nat Comput 17, 183–199 (2018). https://doi.org/10.1007/s11047-017-9657-7

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