Abstract
DNA nanotechnology is an emerging field which utilizes the unique structural properties of nucleic acids in order to build nanoscale devices, such as logic gates, motors, walkers, and algorithmic structures. Predicting the structure and interactions of a DNA device requires effective modeling of both the thermodynamics and the kinetics of the DNA strands within the system. The kinetics of a set of DNA strands can be modeled as a continuous time Markov process through the state space of all secondary structures. The primary means of exploring the kinetics of a DNA system is by simulating trajectories through the state space and aggregating data over many such trajectories. We expand on previous work by extending the thermodynamics and kinetics models to handle multiple strands in a fixed volume, in a way that is consistent with previous models. We developed data structures and algorithms that allow us to take advantage of local properties of secondary structure, improving the efficiency of the simulator so that we can handle reasonably large systems. Finally, we illustrate the simulator’s analysis methods on a simple case study.
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Notes
- 1.
We calculate \(V_0\) as the volume in which we would have exactly one molecule at a standard concentration of 1 mol/L: \(V_0 = 1 / (N_a * 1\,\text{ mol/L })\), where \(N_a\) is Avogadro’s number, and thus \(V_0\) is in liters. Similarly, we may wish to calculate V based on the concentration u in mol/L of a single strand such that the volume V is chosen such that exactly one molecule is present in that volume. In this case we have \(V = \frac{1}{u * N_a}\) and the relative number of states in the box is then \(\frac{V}{V_0} = \frac{N_a}{u * N_a} = \frac{1}{u}\).
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Acknowledgements
We are greatly indebted to years of insights, suggestions, and feedback from Niles Pierce, Robert Dirks, Justin Bois, and Victor Beck, especially their contributions to the formulation of the energy model and the first step simulation mode.This work has been funded by National Science Foundation grants DMS-0506468, CCF-0832824, CCF-1213127, CCF-1317694, and the Gordon and Betty Moore Foundation through the Caltech Programmable Molecular Technology Initiative.
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Schaeffer, J.M., Thachuk, C., Winfree, E. (2015). Stochastic Simulation of the Kinetics of Multiple Interacting Nucleic Acid Strands. In: Phillips, A., Yin, P. (eds) DNA Computing and Molecular Programming. DNA 2015. Lecture Notes in Computer Science(), vol 9211. Springer, Cham. https://doi.org/10.1007/978-3-319-21999-8_13
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