1. Localized DNA Circuits Hieu Bui 1

2. Outline  Localized Kinetics & Modelling  Localized Hybridization Reactions  On Nanotracks  On DNA Origami 2

3. References 3  N. Dalchau, H. Chandran, N. Gopalkrishnan, A. Phillips, J. Reif, Probabilistic Analysis of Localized DNA Hybridization Circuits. Acs Synth Biol 4, 898-913 (2015).  H. Bui, S. Garg, R. Mokhtar, T. Song, J.Reif, Localized Cascade DNA Hybridization Chain Reactions of DNA Hairpins on a DNA Track.  H. Chandran, N. Gopalkrishnan, A. Phillips, J. Reif, Localized Hybridization Circuits. Lect Notes Comput Sc 6937, 64-83 (2011).  M. R. Lakin, R. Petersen, K. E. Gray, A. Phillips, in Lect Notes Comput Sc. (Springer, 2014), pp. 132-147.  M. Teichmann, E. Kopperger, F. C. Simmel, Robustness of Localized DNA Strand Displacement Cascades. Acs Nano, (2014).  J. Elezgaray et al., Connecting Localized DNA Strand Displacement Reactions. Nanoscale, (2015).  E. Kopperger, T. Pirzer, F. C. Simmel, Diffusive transport of molecular cargo tethered to a DNA origami platform. Nano letters 15, 2693-2699 (2015).

4. Objective  Challenges from programing DSD devices:  Speed  Scalability  Spurious interactions/crosstalk  What are the current options?  Sequence design (mismatch, clamp, G-C)  Lower concentration  Developing software  to ease the sequence design process  to track all possible reaction pathways  Programming DSD devices on 2D surface 4

5. A Biophysical Model 5 Local concentration estimation: Distance between molecules Flexibility of DNA Length of molecules

6. Software: How to solve it?  Visual DSD:  To design and analyze DNA strand displacement systems in solution-phase.  Not applicable for 2D DNA circuits.  Need to employ continuous-time Markov chain (CTMC) to be relevant.  PRISM:  To test logical queries by probabilistic model checking. 6

7.  Integrate probabilistic model checking within Visual DSD.  Streamline approach to analyze modifications to a given model.  Optimize the computation of probabilistic queries at multiple time points. Visual DSD PRISM 7

8. How to calculate transient probabilities?  PRISM:  Uniformization method: a discrete time conversion of CTMC to calculate the probability of being in a particular state at a particular time.  High setup cost when requesting multiple time points.  More efficient and stable routine for single calculations.  Visual DSD  Numerical integration of the chemical master equation (CME).  Propagate the solution at a previous time point to the next one.  Low setup cost when requesting multiple time points.  Consume large memory to store multiple time points. 8

9. Chemical Master Equations (CME)  Distribution of all possible trajectories.  Analysis of CME:  Generate a CTMC (full state space of the system).  Each state – a vector of species populations.  Each position – a separate species.  Examples:  Global setting: N species and 1000 copies of each species: state space of 1000 N.  Localized setting: N species and a single copy of each species (present or absent), state space of 2 N. 9

10.  The state space is O(c N ) for N distinct species. (c = 2)  The state space is O(c N ) for N distinct species (c = 1000). 10

11. Visual DSD  To simulate the localized strand displacement circuit:  Generate a CTMC (a detailed mode and an infinite mode).  Transition rates 11

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13. Designed Localized Circuits 13

14. Implementing OR 14

15. Implementing OR 15

16. Implementing AND 16

17. Implementing FANOUT 17

18. More Complex Circuits 18

19. More Complex Circuits 19

20. Simulating Biophysical Model 20

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22. Localized Hybridization Reactions on Nanotracks 22

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24. Experimental Data: Speedup 24

25. Experimental Data 25

26. Experimental Data: Concentration Test 26

27. 27 Localized Hybridization Reactions on DNA Origami

28. 224 x 2 binding sites 28 √ √ √ √ √ √ √ √

29. Consideration  Staples are missing 7% of the time.  75% of 4 gates to be formed.  Built-in redundancy.  Consensus methods.  Hairpins interacting during anneal processes.  Hairpin structure is stable at a higher temperature. 29

30. Abstract Modelling of Tethered DNA Circuits 30

31. Robustness of Localized DNA Strand Displacement Cascades 31

32. Connecting Localized DNA Strand Displacement Reactions 32

33. Diffusive transport of molecular cargo tethered to a DNA origami platform 33