Recent Research in DNA Computing John Reif Dept

Recent Research in DNA Computing John Reif Dept Computer Science Duke University Reif’s DNA Self-Assembly Group Current Ph. D Graduate Students Visiting Scholars: Abeer Eshra Reem Mokhtar Shalin Shah Prior Recent Ph. D Graduate Students Xin Song Hieu Bui Nikhil Gopalkrishnan Peng Yin Tianqi Song Harish Chandran Urmi Majumder Sudhanshu Garg Dan Fu Ming Yang

2 Organization of Talk • Localized DNA Computation: Faster and Simpler Molecular-Scale Computing • Programming DNA-based Biomolecular Reaction Networks on Cancer Cell Membranes: localized circuits, molecular reaction networks • Compact and Fast DNA Logic Circuits Using Strand-Displacing Polymerase and Single-Stranded Logic Gates: logic circuits, enzyme-based circuits • DNA-based Analog Computing: analog circuits

Localized DNA Computation Hieu Bui and John Reif • Linear Cascade DNA Hybridization Chain Reactions (in solution, not localized) • Localized DNA Hybridization Chain Reactions on DNA Tracks • Localized DNA Hybridization Chain Reactions on DNA Origami 3

4 Localized DNA Computation [Hieu Bui and John Reif] • Hieu Bui, Sudhanshu Garg, Reem Mokhtar, Harish Chandran, Vincent Miao and John Reif, Design and Analysis of Localized DNA Hybridization Chain Reactions, Small (2017), 1602983. DOI: 10. 1002/smll. 201602983 • Hieu Bui, Sudhanshu Garg, Vincent Miao, Tianqi Song, Reem Mokhtar, and John Reif, Design and Analysis of Linear Cascade DNA Hybridization Chain Reactions Using DNA Hairpins, Special Issue, Journal of New Physics, Vol. 19, (2017) 015006. doi: 10. 1088/1367 -2630/aa 53 d 0 • Hieu Bui, Shalin Shah, Reem Mokhtar, Tianqi Song, Sudhanshu Garg, John Reif, Localized DNA Hybridization Chain Reactions on DNA Origami, ACS Nano, Volume 12, Num. 2, pp 1146– 1155(January 22, 2018). DOI: 10. 1021/acsnano. 7 b 06699259. • Hieu Bui and John H Reif, Localized DNA Computation, Chapter 19 in book: “From Parallel to Emergent Computing” (Edited by Andrew Adamatzky, Selim Akl, and Georgios Ch. Sirakoulis), CRC Press (February 18, 2019). Taylor & Francis Group of CRC Press. ISBN: 9781138054011 • Sudhanshu Garg, Hieu Bui, Abeer Eshra, Shalin Shah and John H Reif, Nucleic Acid Hairpins: A Robust and Powerful Motif for Molecular Devices, Chapter 7 in book: “Soft Nanomaterials” (Edited by Ye Zhang), World Scientific, (2019).

5 Motivations • DNA – programmable, predictable, and selfassembly. • DNA circuits (AND, OR, NOT, etc. ) – versatile, inexpensive, capable of parallel computing. • The locality effect may speedup the reactions. • Faster switching time compared to regular DNA hybridization reactions. • Minimal leakages due to the physical constraints. • Reusable sequences (gates) - scalable B-DNA (10. 5 bp, 0. 34 nm/bp, 2 nm diameter)

Linear Cascade DNA Hybridization Chain Reactions (in solution, not localized) • Autonomous reaction of controlled self-assembly. v Components of the linear cascade DNA hybridization chain reaction system consisting of 9 metastable DNA hairpins. Hieu Bui, Sudhanshu Garg, Vincent Miao, Tianqi Song, Reem Mokhtar, John Reif 2017 New J. Phys. 19 015006 6 • Hairpins 1– 9 are stable in the absence of initiator I. • The initiator binds at the sticky end of H 1 and undergoes an unbiased strand displacement interaction to open the hairpin. • The newly exposed sequestered sticky end of H 1 binds to the external sticky end of H 2 and opens the hairpin to expose a sequestered sticky end on H 2. • This cascade reaction continues until H 9 is opened. • The designed product is a linear chain formed by staggered hybridization of nine hairpins.

7 Linear Cascade DNA Hybridization Chain Reactions (in solution, not localized) (A) (B) v Simulation results of various linear cascade reaction lengths. The length depends on the number of hairpins involved in each reaction. v Simulation conditions are specified as the following: 5 n. M concentration of hairpins, 6. 5 n. M concentration of reporter complex, 10 n. M concentration of initiator, and the rate constant of displacing the reporter complex is common across all simulation experiments. v Linear cascade reactions when the rate constant is 105 M− 1 s− 1 (A) versus 1. 3 × 106 M− 1 s− 1 (B). Simulation is performed based on the assumption that all hairpin–hairpin pairs follow the second order(bimolecular) chemical reaction. Hieu Bui, Sudhanshu Garg, Vincent Miao, Tianqi Song, Reem Mokhtar, John Reif 2017 New J. Phys. 19 015006

Linear Cascade DNA Hybridization Chain Reactions (in solution, not localized) • Native PAGE gel of different linear cascade reactions involving 2 hairpins with and without addition of target DNA initiator. (A) • Native PAGE gel of different linear cascade reactions involving 4 hairpins with and without addition of target DNA initiator. (B) • Native PAGE gel of different linear cascade reactions involving 6 hairpins with and without addition of target DNA initiator. (C) A B C Hieu Bui, Sudhanshu Garg, Vincent Miao, Tianqi Song, Reem Mokhtar, John Reif 2017 New J. Phys. 19 015006 8

Linear Cascade DNA Hybridization Chain Reactions (in solution, not localized) A 9 • Kinetic characterization of the linear cascade DNA hybridization chain reactions. All samples were prepared at 5 n. M of hairpin with 6. 5 n. M of reporter complex. • (A) Schematic of LCR system before and after interacting with the reporter complex. • (B) Effect of initiator concentration on the rate of linear cascade reaction. Hairpins do not hybridize in the absence of initiator(9 hairpins + 0× I, black). The linear cascade reaction occurs in the presence of 1× initiator concentration (9 hairpins + 1× I, red). The linear cascade reaction occurs at the same rate in the presence of excess initiator(9 hairpins + 8× I, green). B Hieu Bui, Sudhanshu Garg, Vincent Miao, Tianqi Song, Reem Mokhtar, John Reif 2017 New J. Phys. 19 015006 C • (C) Effect of hairpin concentration on the rate of crosstalk and leak reactions: 5 n. M (black curve), 25 n. M (red curve), and 50 n. M (green curve)without the presence of initiator.

Linear Cascade DNA Hybridization Chain Reactions (in solution, not localized) • Effect of the number of hairpins on the rate of linear cascade reaction: 1 hairpin (black curve), 2 hairpins(red curve), 4 hairpins(green curve), 6 hairpins(blue curve), 9 hairpins(cyan curve). Note: the dotted horizontal line indicates the half-life of the linear cascade reaction (the time required for the reaction to reach 50% completion). Inset shows the real-time kinetic of all linear cascade reactions at equilibrium. Hieu Bui, Sudhanshu Garg, Vincent Miao, Tianqi Song, Reem Mokhtar, John Reif 2017 New J. Phys. 19 015006 v Empirical projection of the half-time completion as a function of hairpins. Note: each circle is an experimental result corresponding to the number of hairpins participating in the linear cascade reaction; a blue line is a fitted curve from those circles. 10

11 Localized DNA Hybridization Chain Reactions on DNA Tracks • Components of localized DNA hybridization chain reaction system: six metastable DNA hairpins anchored to a long DNA track via Ai domains. Prior to the addition of the initiator, DNA hairpins do not hybridize and are sequestered in the inactive states. • Triggered self-assembly of localized DNA hybridization chain reaction mechanism for the first and last steps upon sensing the presence of the catalyst / initator. Bui, H. , Miao, V. , Garg, S. , Mokhtar, R. , Song, T. , Reif, J. , Small 2017, 13, 1602983.

12 Localized DNA Hybridization Chain Reactions on DNA Tracks • Fluorescence reporting mechanism to observe the kinetics of localized DNA hybridization reaction. A FRET pair consists of a fluorescence donor (green) and a fluorescence quencher (black). Upon sensing the completion, the FRET pair is disrupted by the last hairpin, giving rise to an increase in the fluorescence emission. Bui, H. , Miao, V. , Garg, S. , Mokhtar, R. , Song, T. , Reif, J. , Small 2017, 13, 1602983.

13 Localized DNA Hybridization Chain Reactions on DNA Tracks A B C • Kinetic characterization of triggered self-assembly hybridization chain reactions. • A) Localized DNA hybridization chain reactions with and without the presence of the long DNA track in two times excess initiators. Note: inset shows the fluorescence responses of the same systems but in the absence of the initiator. • B) Effect of localized DNA hybridization chain reaction rate as a function of initiator concentration. • C) Control kinetic analysis of reactions as a function of hairpins in the absence of long DNA track. Bui, H. , Miao, V. , Garg, S. , Mokhtar, R. , Song, T. , Reif, J. , Small 2017, 13, 1602983.

14 Localized DNA Hybridization Chain Reactions on DNA Tracks • Fluorescence experimental results of the two systems which are then used to quantify the speed -up from tethering DNA hairpins on the DNA track: • A) six DNA hairpins (no anchor domain, no track) in the presence of 2× initiators • B) six DNA hairpins bound to the long DNA track in the presence of 2× initiators. • Note: Dashed lines indicate half-time completion—the time required for the reaction to reach 50% completion. • C) Model to describe cascade reactions with and without the locality effect. • Note: AND symbol indicates bimolecular reaction; TRIANGLE symbol indicates unimolecular reaction Bui, H. , Miao, V. , Garg, S. , Mokhtar, R. , Song, T. , Reif, J. , Small 2017, 13, 1602983.

15 Localized DNA Hybridization Chain Reactions on DNA Origami • DNA origami rectangle with modified staple strands (green circles). Metastable DNA hairpins tethering to DNA origami rectangle’s surface via modified staple strands through the anchor domains. v Mechanism of DNA hybridization reactions on DNA origami surface. Metastable DNA hairpins tethering to DNA origami rectangles via modified staple strands. Upon sensing the presence of the target initiator, the chain reactions occur among the hairpins, releasing the encoded information in the last hairpin. Hieu Bui, Shalin Shah, Reem Mokhtar, Tianqi Song, Sudhanshu Garg, and John Reif ACS Nano 2018 12 (2), 1146 -1155

16 Localized DNA Hybridization Chain Reactions on DNA Origami • AFM images of DNA origami rectangle labeled with DNA hairpins. • Six metastable DNA hairpins self-assembled on DNA origami rectangle (a) • Six metastable DNA hairpins underwent cascade hybridization reactions after adding the initiator (b) • Six metastable DNA hairpins underwent cascade hybridization reactions after adding the biotin-labeled output to detect the reaction completion via binding to the streptavidin molecule (c) Hieu Bui, Shalin Shah, Reem Mokhtar, Tianqi Song, Sudhanshu Garg, and John Reif ACS Nano 2018 12 (2), 1146 -1155

17 Localized DNA Hybridization Chain Reactions on DNA Origami • (a) Illustration of DNA origami used single-molecule TIRF experiment. Blue tokens indicate hairpins while red token indicates marker strand. • (b, c) TIRF images for DNA origami labeled with ATTO 647 N marker and TAMRA initiator. The green channel is for 561 nm laser line (TAMRA label). Similarly, the red channel is for 635 nm laser line (ATTO 647 N label). The approximate Gaussian localized images for both the channels. These images are analyzed for co-localization independent of the dynamic range values and noise. • (d) Co-localized image where yellow spots (highlighted in green boxes) representing DNA origami with hairpins. • Scale bars are 5 μm. Hieu Bui, Shalin Shah, Reem Mokhtar, Tianqi Song, Sudhanshu Garg, and John Reif ACS Nano 2018 12 (2), 1146 -1155

18 Localized DNA Hybridization Chain Reactions on DNA Origami • a) Illustration of DNA origami used single-molecule TIRF experiment. Blue tokens indicate hairpins while red token indicates marker strand. • (b, c) TIRF images for DNA origami labeled with ATTO 647 N marker dye and ATTO 488 output. The blue channel is for 488 nm laser line (ATTO 488 label). Similarly, the red channel is for 635 nm laser line (ATTO 647 N label). The approximate Gaussian localized images for both the channels. • (d) Co-localized image where yellow spots (highlighted in green boxes) indicates DNA origami with reaction completion. • (e) Co-localization analysis for different reaction incubation times to observe kinetics. • Scale bars are 5 μm. Hieu Bui, Shalin Shah, Reem Mokhtar, Tianqi Song, Sudhanshu Garg, and John Reif ACS Nano 2018 12 (2), 1146 -1155

19 Localized DNA Hybridization Chain Reactions on DNA Origami • (a) Schematic of localized cascade DNA hybridization chain reaction on the surface of DNA origami rectangle before and after the completion. • (b) Kinetic characterization of localized cascade DNA hybridization chain reaction on DNA origami rectangle (green curve). Kinetic characterization of cascade DNA hybridization chain reaction without DNA origami rectangle (purple curve). Each solution was kept at 5 n. M concentration and the initiator was added in 2× excess. • (c) Effect of localized cascade DNA hybridization chain reaction rate as a function of initiator concentration. Hieu Bui, Shalin Shah, Reem Mokhtar, Tianqi Song, Sudhanshu Garg, and John Reif ACS Nano 2018 12 (2), 1146 -1155

20 Summary of Localized Linear Cascade Results • Design, simulation, and synthesis of linear cascade DNA hybridization chain reactions. • 9 distinct hairpins underwent cascade hybridization chain reactions upon sensing the presence of the target initiator. • Design, simulation, and synthesis of linear cascade DNA hybridization chain reactions on DNA tracks. • 6 distinct hairpins underwent cascade hybridization chain reactions • The speedup was observed due to the locality effect. • Design, simulation, and synthesis of linear cascade DNA hybridization chain reactions on DNA origami. • 6 distinct hairpins underwent cascade hybridization chain reactions • The speedup was observed due to the locality effect, consisting with prior studies. • Proof-of-concept examples which can be applied to other surfaces to utilize the locality effect. • Combination with other DNA circuits to carry out surface DNA computation.

21 Organization of Talk • Localized DNA Computing • Programming DNA-based Biomolecular Reaction Networks on Cancer Cell Membranes • Compact and Fast DNA Logic Circuits Using Strand-Displacing Polymerase and Single-Stranded Logic Gates • DNA-based Analog Computing

Programming DNA-based Biomolecular Reaction Networks on Cancer Cell Membranes Tianqi Song and John Reif Tianqi Song, Hieu Bui, Sudhanshu Garg, Abeer Eshra, Daniel Fu, Shalin Shah, Ming Yang, Reem Mokhtar, and John Reif, Programming DNA-Based Biomolecular Reaction Networks on Cancer Cell Membranes, submitted for publication(2019) 22

23 DNA-based Biomolecular Reaction Networks on Cancer Cell Membranes initiator output DNA strand displacement reactions D Song et al. (2019) In submission

24 Goals, Principles and Solutions Song et al. (2019) In submission

25 Node Design DNA strand displacement reaction • Two modules: reaction module (DNA hairpin) and addressing module. • Two modules are paired by the hybridization between domains A and A*. sgc 4 f is an aptamer to target a particular cell membrane receptor. Song et al. (2019) In submission

26 Cascade Reaction Abstraction: initiator sgc 4 f sgc 8 c output Song et al. (2019) In submission

27 Capability and Applications • • Linear cascades Complex reaction networks Logic circuits Cancer cell recognition and therapies Song et al. (2019) In submission

28 Linear Cascades Cancer Cell Lines: sgc 4 f Ramos CCRF-CEM sgc 8 c TC 01 sgc 4 f sgc 8 c TD 08 TC 01 TE 13 TD 08 TC 01 Flow cytometry results: high ratios (in fluorescence intensity) between Cellwith circuit and Cellonly (data from three repeats). Song et al. (2019) In submission

A Reaction Network on CCRF-CEM 29 sgc 8 c sgc 4 f TE 13 TC 01 TE 17 Path 1 TC 01 sgc 4 f sgc 8 c Path 2 TC 01 TE 13 sgc 8 c Path 3 TE 17 sgc 4 f sgc 8 c Path 4 TE 17 TE 13 sgc 8 c Song et al. (2019) In submission

Control Experiments 30 Low ratios (in fluorescence intensity) between Cellwith reporter and Cellonly (data from three repeats). Song et al. (2019) In submission

31 Logic Computing and Cancer Cell Recognition sgc 4 f AND sgc 8 c sgc 4 f sgc 8 c Aptamers (Receptors) Cell Lines sgc 4 f sgc 8 c CEM yes He. La yes no Ramos no yes K 562 no no Low ratios are expected for He. La, Ramos and K 562. Song et al. (2019) In submission

32 Further On-Going Work • Cancer therapies: output of a circuit opens a DNA-based capsule containing drug molecules. • Distributed computing among different cell types.

33 Organization of Talk • Localized DNA Computing • DNA-based Analog Computing: analog circuits • Compact and Fast DNA Logic Circuits Using Strand-Displacing Polymerase and Single-Stranded Logic Gates: logic circuits, enzyme-based circuits

Localized DNA Computation Tianqi Song and John Reif • Compact and Fast DNA Logic Circuits Using Strand-Displacing Polymerase and Single-Stranded Logic Gates • DNA-based Analog Computing • Programming DNA-based Biomolecular Reaction Networks on Cancer Cell Membranes 34

Compact and Fast DNA Logic Circuits Using Strand -Displacing Polymerase and Single-Stranded Logic Gates 35 [Tianqi Song and John Reif] Tianqi Song, Abeer Eshra, Shalin Shah, Hieu Bui, Daniel Fu, Ming Yang, Reem Mokhtar, and John Reif, Fast and Compact DNA Logic Circuits Based on Single-Stranded Gates Using Strand-Displacing Polymerase, in submission (2019) Song et al. (2019) In submission

Motivation 36 Reduce complexity Improve speed news. mit. edu Song et al. (2019) In submission

37 Goals, Principles and Solutions Song et al. (2019) In submission

38 Single-Stranded Logic Gates: OR Gate Design and Performance Gate Strands Prepared by Fuel F Two Reaction Paths to Produce Output in OR Gate Each gate strand is at 1 x (1 x = 100 n. M). Each input strand is at 1 x when encoding “ 1”, otherwise 0 x. Each domain is 30 nt long. Reporting Reaction Song et al. (2019) In submission

39 Single-Stranded Logic Gates: AND Gate Two Reaction Paths to Produce Output in AND Gate Design and Performance d Path 1 Each gate strand is at 1 x (1 x = 100 n. M). Each input strand is at 2 x when encoding “ 1”, otherwise 0 x. Path 2 Side Reaction in AND Gate waste Song et al. (2019) In submission

40 2 -Layer Cascades 1 x 2 x 1 x 1 x Rule of cascading: a gate should always produce enough output for its downstream gates. Song et al. (2019) In submission

41 3 -Layer Cascades 2 x 2 x 1 x 1 x Song et al. (2019) In submission

42 Fan-in and Fan-out Output O 1 4 x 1 x 1 x 1 x Song et al. (2019) In submission

43 A Square-Root Circuit Dual-rail Logic Circuit 2 x 1 x 1 x 2 x 2 x 1 x Dual-rail logic (as in Qian et al. (2011) Science), each variable in the original circuit is represented by two corresponding variables in the circuit of dual-rail logic format. For example, variable “A” is represented by two variables “A -0” and “A-1” in the dual-rail logic circuit: A is logic “ 1” > A-1 is logic “ 1”, A-0 is logic “ 0”; A is logic “ 0” > A-1 is logic “ 0”, A-0 is logic “ 1”. Song et al. (2019) In submission

A Square-Root Circuit 44 Song et al. (2019) In submission

45 Signal Amplification and Restoration Once every several layers For nonideal inputs to a circuit Song et al. (2019) In submission

46 Discussion • Further improvements: more compact mechanism of signal restoration. • Future work: dynamical circuits (using only polymerase) like oscillators, controllers, etc.

47 Organization of Talk • Localized DNA Computing • Compact and Fast DNA Logic Circuits Using Strand-Displacing Polymerase and Single-Stranded Logic Gates • Programming DNA-based Biomolecular Reaction Networks on Cancer Cell Membranes • DNA-based Analog Computing

48 DNA-based Analog Computing Tianqi Song and John Reif Tianqi Song, Sudhanshu Garg, Hieu Bui, Reem Mokhtar, and John H Reif, Design and Analysis of Compact DNA Strand Displacement Circuits for Analog Computation Using Autocatalytic Amplifiers, ACS Synthetic Biology (Dec 2017). DOI: 10. 1021/acssynbio. 6 b 00390 Daniel Fu, Shalin Shah, Tianqi Song and John H Reif, DNA-based Analog Computing, Chapter in book: Synthetic Biology: Methods and Protocols, Edited by effrey C. Braman), In Series Methods in Molecular Biology, published by Springer, pp. 411 -417 (2018). ISBN 978 -1 -4939 -7795 -6 Tianqi Song, Sudhanshu Garg, Hieu Bui, Reem Mokhtar, and John H. Reif, Analog Computation by DNA Strand Displacement Circuits, ACS Synthetic Biology, 5, 898− 912 (July, 2016). DOI: 10. 1021/acssynbio. 6 b 00144

49 Motivation • Processing continuous signal directly • Compact circuits for cellular sensing

50 Two Architectures • The first architecture: circuits for basic arithmetic operations (addition, subtraction and multiplication) and polynomials. • The second architecture: compact circuits to compute functions like sqrt(x), ln(x), and exp(x).

51 Analog Computation by DNA Strand Displacement Circuits Daniel Fu, Shalin Shah, Tianqi Song and John H Reif, DNA-based Analog Computing, Chapter in book: Synthetic Biology: Methods and Protocols, Edited by effrey C. Braman), In Series Methods in Molecular Biology, published by Springer, pp. 411 -417 (2018). ISBN 978 -1 -4939 -7795 -6 Tianqi Song, Sudhanshu Garg, Hieu Bui, Reem Mokhtar, and John H. Reif, Analog Computation by DNA Strand Displacement Circuits, ACS Synthetic Biology, 5, 898− 912 (July, 2016). DOI: 10. 1021/acssynbio. 6 b 00144

52 Analog Gates: Addition Gate DNA design Abstraction pa = a 1 + a 2. High-level CRN model [Ia 1]0 = a 1, [Ia 2]0 = a 2. [Oa]∞ = pa. [Ga 1]0 = [Da 1]0 = [Ga 2]0 = [Da 2]0 = ra, and [Fa]0 = 2 ra where (0, ra) is the input range. Unit of concentration is 5 n. M. Song et al. (2016) ACS Synthetic Biology

DNA Reactions in Addition Gate 53 Song et al. (2016) ACS Synthetic Biology

Analog Gates: Subtraction Gate Abstraction 54 DNA design ps = s 1 - s 2 (s 1 > s 2 ). High-level CRN model [Is 1]0 = s 1, [Is 2]0 = s 2. [Is 1]∞ = ps. [Gs]0 = [Ds]0 = rs, where (0, rs) is the input range. Song et al. (2016) ACS Synthetic Biology

55 DNA Reactions in Subtraction Gate Song et al. (2016) ACS Synthetic Biology

Abstraction DNA design 56 Analog Gates: Multiplication Gate High-level CRN model pm = m 1 * m 2. [Im 1]0 = m 1, [Im 2]0 = m 2. [Om]∞ = pm. [Fm 1]0 = [Gm 1]0 = [Dm 1]0 = [Fm 2]0 = [Gm 3]0 = [Dm 3]0 = [Gm 4]0 = rm, where (0, rm) is the input range. Song et al. (2016) ACS Synthetic Biology

Mechanism of Multiplication Gate 57 Set up the concentration ratio between [G’m 3] and [Gm 4] (fast) Produce Im 1 a (slow) Im 1 a is distributed according to concentration ratio Amplify Om 1 for rm times. Song et al. (2016) ACS Synthetic Biology

DNA Reactions in Multiplication Gate 58 Song et al. (2016) ACS Synthetic Biology

59 DNA Reactions in Multiplication Gate Song et al. (2016) ACS Synthetic Biology

60 Simulation Results Addition, subtraction and multiplication gates of input range (0, 4). The color represents log 2(t) where t is the time (seconds) that the output stays in the valid output range (a range of ± 5% error). Song et al. (2016) ACS Synthetic Biology

61 Computing Polynomials (a) Execution of the circuit to compute f(x) when x = 0. 7. (b) Performance of the circuit to compute f(x), where t is the time (seconds) that the output stays in the valid output range. A circuit to compute f(x) = 1 + x 2/2! + x 3/3! for 0 < x < 1. Song et al. (2016) ACS Synthetic Biology

62 Design and Analysis of Compact DNA Strand Displacement Circuits for Analog Computation Using Autocatalytic Amplifiers Tianqi Song and John Reif] Tianqi Song, Sudhanshu Garg, Hieu Bui, Reem Mokhtar, and John H Reif, Design and Analysis of Compact DNA Strand Displacement Circuits for Analog Computation Using Autocatalytic Amplifiers, ACS Synthetic Biology (Dec 2017). DOI: 10. 1021/acssynbio. 6 b 00390

63 DNA-based Slide Rule http: //www. sliderulemuseum. com https: //www. digitaltrends. com/

64 Computing Square Root Compute sqrt(x) Slide rule Our architecture Step 1 Step 2 Step 3 ln(x) 0. 5*ln(x) = ln(x 0. 5) exp(ln(x 0. 5)) = x 0. 5 = sqrt(x) a 1 ln(x) exp(a 2(a 1 ln(x))) = exp(a 2 a 1 ln(x))) = xa 1*a 2 For our architecture, step 1 and step 2+3 are done by DNA amplifiers. We program the amplifiers such that a 1*a 2 = 0. 5. Song et al. (2018) ACS Synthetic Biology

65 The Architecture Output Module Input Module I R 4 R 1 Input and output: R 2 I is the input DNA strand [I]0 is the input value x. O is the output DNA strand [O]∞ is the output value. O R 3 Stopper Modules: Input module: starts to work since the beginning, computes the time (using the input x) t (to trigger the stopper module) to stop the output module immediately; Output module: starts to work since the beginning, produces the output strand until time t; Stopper module: starts to work once triggered, stops the output module from producing the output strand. Song et al. (2018) ACS Synthetic Biology

66 Modules and Reactions Output Module Input Module I • The input module produces DNA strand I* (by [I*] = f(t)) to consume input strand I by reaction R 1, and it starts to work since t = 0; R 4 R 1 R 2 R 3 Stopper Module O • The output module produces DNA strand O (by [O] = g(t)) by reaction R 4 , and it starts to work since t = 0; • The stopper module only starts to work when it is triggered by I* via reaction R 2. R 1 and R 2 compete on I*. If we let R 1 be much faster than R 2, R 2 will start to work to trigger the stopper module only when all input strand I has been consumed (and then R 1 has to stop) at the moment t = f-1(x). Once the stopper module is triggered, it reacts quickly and stops the output module immediately via a fast reaction R 3. Song et al. (2018) ACS Synthetic Biology

Computing a Function Output Module Input Module I R 4 R 1 R 2 R 3 Stopper Module O 67 The circuit works as this: t = 0: The input module starts to produce I* to consume input strand I by reaction R 1. The output module starts to produce output strand O by reaction R 4. t = f-1(x): All input strand I has been consumed and R 1 has to stop. R 2 starts and triggers the stopper module. The stopper module stops the output module immediately. The output module stops and has produced g(f-1(x)) concentration of output strand O, which means [O]∞ = g(f-1(x)). Tune the input and output modules such that [O]∞ = g(f-1(x)) = K(x), where K(x) is the function that we want to compute. Song et al. (2018) ACS Synthetic Biology

68 Example of Computing Sqrt(x) Song et al. (2018) ACS Synthetic Biology

69 Need a DNA circuit (as a motif for the modules) that produces an exponential output by β*exp(α t) (in a certain time domain), and α can be easily tuned by changing the concentrations of some components in the circuit. Song et al. (2018) ACS Synthetic Biology

70 Modules Implemented by a DNA Amplifier A DNA amplifier that has a tunable exponential output (concentration of Of) in a certain time domain. The exponent can be tuned by changing the concentrations of F 1 and F 2. Song et al. (2018) ACS Synthetic Biology

71 Output of the Amplifier (a) How f(t) = [Of] grows over time. In the simulation, we let the initial concentrations be [G 1]0 = [G 2]0 = 100 n. M, [F 1]0 = [F 2]0 = 200 n. M, [H]0 = [F]0 = 100 n. M. (b) In time domain [t 1, t 2] (seconds), where t 1 = 3 × 105 and t 2 = 3. 5 × 105, f(t) can be well approximated by an exponential function e(t) = 0. 48 × exp(8. 51× 10 – 6)t. Song et al. (2018) ACS Synthetic Biology

72 Simulation Results (a) The simulated performance of the circuit to compute sqrt(x), x ∈ [6. 15, 9. 42] (n. M): the simulation is conducted for samples {6. 15, 6. 25, . . . , 9. 35}. (b) The simulated performance of the circuit to compute ln(x), x ∈ [6. 15, 9. 42] (n. M): the simulation is conducted for samples {6. 15, 6. 25, . . . , 9. 35}. (c) The simulated performance of the circuit to compute exp(x), x ∈ [0. 79, 1. 22] (n. M): the simulation is conducted for samples {0. 79, 0. 80, . . . , 1. 22}. Song et al. (2018) ACS Synthetic Biology

73 Summary • Localized DNA Computation: Faster and Simpler Molecular-Scale Computing • Programming DNA-based Biomolecular Reaction Networks on Cancer Cell Membranes: localized circuits, molecular reaction networks • Compact and Fast DNA Logic Circuits Using Strand-Displacing Polymerase and Single-Stranded Logic Gates: logic circuits, enzyme-based circuits • DNA-based Analog Computing: analog circuits

Reif Group Papers on the Web Reif Papers on DNA nanoscience on the Web: - http: //www. cs. duke. edu/~reif/vita/papers. html - Survey on DNA Computation: Hieu Bui, Harish Chandran, Sudhanshu Garg, Nikhil Gopalkrishnan, Reem Mokhtar, Tianqi Song and John H Reif, DNA Computing, Chapter in Section 3: Architecture and Organization, Volume I: Computer Science and Software Engineering (Edited by Teofilo F. Gonzalez), The Computer Science Handbook, Third Edition (Editor. In-Chief Allen B. Tucker), Taylor & Francis Group, (2014). Other Reif Papers on the Web: - http: //www. cs. duke. edu/~reif/vita/papers. html

Talks Downloadable from Reif’s Website - www. cs. duke. edu/~reif/paper/DNA-Nanoscience. Talks This Talk: DNA-Based Programmable Molecular Devices http: //www. cs. duke. edu/~reif/paper/DNA-Nanoscience. Talks/DNA-Molecular. Devices/DNA -Molecular. Devices. pdf Other Talks: DNA Computing: Theory, Experiments & Software: http: //www. cs. duke. edu/~reif/paper/DNA-Nanoscience. Talks/DNA-Computing. pdf Self-Assembled DNA Nanostructures: www. cs. duke. edu/~reif/paper/DNA-Nanoscience. Talks/DNA-Nanostructures. pdf DNA-Based Programmable Autonomous Molecular Robotic Devices: www. cs. duke. edu/~reif/paper/DNA-Nanoscience. Talks/DNA-Prog. Auto. Mol. Robotics/DNAProg. Auto. Mol. Robotics. pdf

76 Thank You!