DNA Reaction Networks Fueled by Strand Displacement Hieu

DNA Reaction Networks Fueled by Strand Displacement Hieu Bui 1

Outline • Yurke-Tuberfield's DNA Tweezers: the invention of toe-hold mediated strand displacement • Yurke: Catalytic Tweezers • Winfree's Seesaw Gates • Zhang's DNA Reaction Networks • Zhang’s Allosteric DNA Catalytic Reactions • Zhang’s DNA Catalytic Reactions • Soloveichik's DNA Chemical Kinetics • Cardelli's DNA Strand Algebraciruits 2

Toehold mediated strand displacement 3

Example of Toehold mediated strand displacement 4

Details of Toehold mediated strand displacement 5

Toehold mediated strand displacement vs toehold mediated strand exchange (where original strand melts off) 6

Example of Toehold mediated strand exchange 7

Multiple States of Toehold mediated strand displacement 8

Kinetics of Toehold mediated strand displacement and exchange (Zhang and Winfree) 9

Strand Displacement G°ABC , G°r. ABC , G°l. ABC ΔG°r = G°r. ABC - G°ABC ΔG°l = G°l. ABC - G°ABC Nearest neighbor model Pr α exp(-ΔG°r /RT) Pl α exp(-ΔG°l /RT)

Open Position Yurke-Tuberfield's DNA Tweezers: the invention of toe-hold mediated strand displacement Yurke, B. , Turberfield, A. J. , Mills, A. P. , Simmel, F. C. & Neumann, J. L. A DNA- fuelled molecular machine made of DNA. Nature 406, 605– 608 (2000). 11

Energetics of Yurke-Tuberfield's DNA Tweezers Closed Position Fuel Waste Open Position 12

Rotary device using PX–JX 2 junctions controlled by toe-hold mediated strand displacement Position 1 Position 2 Yan, H. , Zhang, X. P. , Shen, Z. Y & Seeman, N. C. A robust DNA mechanical device controlled by hybridization topology. Nature 415, 62– 65 (2002). 13

Qian L , Winfree E J. R. Soc. Interface doi: 10. 1098/rsif. 2010. 0729 Seesaw Gates: use of toe-hold mediated strand exchange 14

Qian L , Winfree E J. R. Soc. Interface doi: 10. 1098/rsif. 2010. 0729 Details of Seesaw Gates The DNA motif for ‘seesaw’ gates. (a) Abstract gate diagram. Red numbers indicate initial concentrations. (b) The DNA gate motif and reaction mechanism. S 1, S 2, S 3 and S 4 are the recognition domains; T is the toehold domain; T′ is the Watson– Crick complement of T, etc. Arrowheads mark the 3′ ends of strands. Signal strands are named by their domains from 3′ to 5′, i. e. from left to right, so the input is S 1 TS 2; gate base strands and threshold bottom strands are named by their domain from 5′ to 3′. All reactions are reversible and unbiased; solid lines indicate the dominant flows for the initial concentrations shown in (a), while the reverse reactions are dotted. (c) The threshold motif and reaction mechanism. The toehold is extended by a few bases (s′ 1, the complement of the first few 5′ bases of S 1), providing an increased rate constant relative to the gate itself. Branch migration intermediate states are omitted from the diagram. (d) Example sequences. Gate complexes and signal molecules are shown at the domain level (second column) and at the sequence level (third column). Here, recognition domain sequences are 15 nt, the toehold domain sequence is 5 nt, and the toehold is extended by 3 nt for the threshold. Other lengths are possible, so long as they ensure that recognition domains will not spontaneously dissociate, toehold exchange is fast, and thresholding 15 is sufficiently faster.

Qian L , Winfree E J. R. Soc. Interface doi: 10. 1098/rsif. 2010. 0729 Seesaw Gates Abstract diagrams for seesaw gate circuits. (a) The general form of a gate node. Each gate i may be connected to many wires on each side, potentially all N nodes in the network, including itself. For each wire from the right side of gate i to the left side of gate j, the initial concentration of the free signal wi, j may be written above the wire, and the initial concentrations of gate complex gj, i: i (wj, i bound to gate i) and gi: i, j (wi, j bound to gate i) may be written within the node at the ends of the corresponding wires. Gate concentrations are simply omitted if they are zero. Initial concentrations of thj, i: i (the threshold for wj, i arriving at gate i) and thi: i, j (the threshold for wi, j arriving at gate i) may be written in the same locations as gj, i: i and gi: i, j, respectively, but as negative numbers —or omitted if they are zero. (b) The general form of a wire. Each wire is specifically connected on its left end to the right side of a gate node, and connected on its right end to the left side of a gate node. (c) An example circuit with five realized gates (numbered circles), five virtual gates (numbers at ends of wires), and 11 wires. Each wire is identified by the two gates it connects; thus the virtual gates serve to provide full names (and sequences) to their incident wires. Note that circuit diagrams may be drawn without providing gate numbers, as they are not relevant to circuit function. 16

Qian L , Winfree E J. R. Soc. Interface doi: 10. 1098/rsif. 2010. 0729 Seesaw Gates Logical OR Gate Logical AND Gate Circuit diagrams and input/output behaviour of boolean logic gates. Output wires with arrowheads indicate that a downstream load is assumed, which consumes signal strands as they are released. (a−b) A two-input OR gate and a two-input AND gate using, respectively, 1 and 4 seesaw gates, the ‘ 1 -4 scheme’. Circuits constructed using the 1 -4 scheme are not clean, and thus would perform worse if threshold crosstalk and threshold inhibition were modelled. (c–d) A two-input OR gate and a two-input AND gate using two seesaw gates each, the ‘ 2 -2 scheme’. Circuits constructed using the 2 -2 17

Qian L , Winfree E J. R. Soc. Interface doi: 10. 1098/rsif. 2010. 0729 Seesaw Gates for Logic OR and AND 18

Qian L , Winfree E J. R. Soc. Interface doi: 10. 1098/rsif. 2010. 0729 Seesaw Gates Compiling boolean logic circuits. (a) A sample circuit with six gates. (b) Translation into an equivalent dual-rail circuit with 12 gates. (c, d) Translation into an equivalent seesaw gate circuit with 32 gates (1 -4 scheme) and 26 gates (2 -2 scheme). (e, f) Simulation results for all 32 possible input vectors in the 1 -4 scheme and in the 2 -2 scheme. The concentrations of all four dual-rail output species are shown as a function of time. Delays vary with the input, depending the shortest decision path through the network. Simulations were run using the concentration 1 x = 50 n. M, with ON inputs at 0. 9 x and OFF inputs at 0. 1 x. For the 1 -4 scheme, the simulated reaction equations were augmented to also model threshold crosstalk, which degrades the performance of OR gates—but the system still works. 19

Qian L , Winfree E J. R. Soc. Interface doi: 10. 1098/rsif. 2010. 0729 Seesaw Gates A 74 L 85 standard 4 -bit magnitude comparator (four layers deep) and its seesaw circuit simulation, with 1 x = 50 n. M. (a) The digital logic circuit diagram. The corresponding seesaw circuit has roughly 100 seesaw gates. (b) Seesaw circuit simulation with selected input vector of A greater than B. (c) Seesaw circuit simulation with selected input vector of A smaller than B. (d) Seesaw circuit simulation with selected input vector of A equal to B. 20

Qian L , Winfree E J. R. Soc. Interface doi: 10. 1098/rsif. 2010. 0729 Seesaw Gates Implementation of relay circuits. (a) A simple circuit with current source (battery) and controlled device (denoted by a resistor), the corresponding seesaw gate circuit, and its simulation using 1 x = 50 n. M. Shaded and unshaded sides of seesaw gates assist checking that a wire always connects different sides of two seesaw gates as required by node polarity, i. e. each wire connects the shaded side of one seesaw gate to the unshaded side of another. Switching signal A is provided at 1 x if ON, or else 0. 1 x if OFF. Input current signal was provided at 10 x; to verify that no output signal is produced when the current input is OFF, a 1 x signal was provided. (b) AND logic. (c) OR logic. (d) A more complex circuit. Overlapping trajectories (orange and light blue) were shifted to the left by 100 s to make them visible. (e) Switching signal fan-out, current signal fan-out and current signal fanin. 21

LL Qian et al. Nature 475, 368 -372 (2011) doi: 10. 1038/nature 10262 The seesaw gate motif and the construction of linear threshold gates. 22

Qian L , Winfree E J. R. Soc. Interface doi: 10. 1098/rsif. 2010. 0729 Seesaw Gates Analogue time-domain circuits. (a) A catalytic cascade that exhibits initially quadratic growth, with α ≈ 125 h− 2. Temporal trajectories are shown for a series of exponentially decreasing initial input concentrations. (b) A positive feedback circuit that exhibits initially exponential growth, with β ≈ 17 h− 1. The same series of exponentially decreasing input concentrations now yields a series of trajectories with linearly increasing half-completion times. (c) A pulse-generating circuit. Pulse amplitude depends on the input concentration. Here, we use a linear series of input concentrations between 0 x and 1 x. All simulations use 1 x = 50 n. M. 23

Qian L , Winfree E J. R. Soc. Interface doi: 10. 1098/rsif. 2010. 0729 Seesaw Gates Parallel preparation of seesaw gates as hairpin precursors. Using DNA microarray synthesis technologies, each gate, threshold and fuel is made as a single strand. After cleavage from the surface, the mixture is annealed to form hairpins. Restriction enzymes then cleave the hairpins to form gate and threshold complexes. Relative concentrations (red numbers) are set based on the number of DNA chip spots dedicated to a given strand; in this example, one spot produces 0. 25 x. 24

Catalysis is the increase in the rate of a chemical reaction due to the participation of an additional substance called a catalyst A reaction with a Catalysis is a Catalytic Reaction 25

Bernard Yurke, Catalytic DNA Systems, DNATEC 09, 2009 DNA Catalytic Cascades 26

Bernard Yurke, Catalytic DNA Systems, DNATEC 09, 2009 DNA Catalytic Cascades 27

Bernard Yurke, Catalytic DNA Systems, DNATEC 09, 2009 DNA Catalytic Cascades 28

Bernard Yurke, Catalytic DNA Systems, DNATEC 09, 2009 DNA Catalytic Cascades 29

Bernard Yurke, Catalytic DNA Systems, DNATEC 09, 2009 DNA Catalytic Cascades 30

Bernard Yurke, Catalytic DNA Systems, DNATEC 09, 2009 DNA Catalytic Cascades 31

Bernard Yurke, Catalytic DNA Systems, DNATEC 09, 2009 DNA Catalytic Cascades 32

Bernard Yurke, Catalytic DNA Systems, DNATEC 09, 2009 DNA Catalytic Cascades 33

Bernard Yurke, Catalytic DNA Systems, DNATEC 09, 2009 DNA Catalytic Cascades 34

Bernard Yurke, Catalytic DNA Systems, DNATEC 09, 2009 DNA Catalytic Cascades 35

Bernard Yurke, Catalytic DNA Systems, DNATEC 09, 2009 DNA Catalytic Cascades 36

Bernard Yurke, Catalytic DNA Systems, DNATEC 09, 2009 DNA Catalytic Cascades 37

Zhang et al Science 2007, 318 (16), 1121 DNA Reaction Networks 1 4 2 5 6 3 38

Zhang et al Science 2007, 318 (16), 1121 DNA Reaction Networks 1 4 k 0=2. 3 x 101 M-1 s-1 k 1=6. 5 x 105 M-1 s-1 2 5 k 3=4 x 10 -3 s-1 k 2=4. 2 x 105 M-1 s-1 6 3 krox=4 x 105 M-1 s-1 39

Zhang et al Science 2007, 318 (16), 1121 DNA Reaction Networks The entropy-driven reaction. (A) System components. Number labels denote functional domains, which are continuous stretches of DNA that act as units in binding. Domain x is the complement of (and will hybridize to) domain x. (B) The proposed catalytic pathway. Reverse reactions are also present and modeled (with the exception of I 5+OB→I 4, which occurs at a negligible rate). (C) Analysis by PAGE (12% native gel) of the reaction mechanism. Unless otherwise noted, all experiments were performed at 25°C in tris-acetate (TE) buffer supplemented with 12. 5 m. M Mg. Cl 2. Here, [S] = [F] = 200 n. M. [C] = 200 n. M, except where C* denotes 20 n. M. “ann. ” denotes that species were annealed; “ 30 m” denotes that the reaction occurred for 30 min. See fig. S 5 for the full gel, including control lanes. (D) Fluorescent reporter strategy. ROX denotes the carboxy-X-rhodamine fluorophore, and RQ denotes the Iowa Black Red Quencher. Domain 2 is subdivided into 2 a, 2 b, and 2 c; 2 ab consists of 2 a and 2 b (Table 1). (E) Demonstration of catalysis. Different amounts of C were introduced into the system at t ≈ 0. Here, [S] = 10 n. M = 1×, [F] = 13 n. M, and [OR] = 30 n. M. Fluorescence (in all figures) is reported in units such that 0. 0 is the background fluorescence of the quenched reporter and 1. 0 is the fluorescence of ∼ 10 n. M of triggered reporter. The control trace (black) shows the reaction with no substrate S and no catalyst C. Dotted lines show curves calculated with the reduced reaction model. sim, simulated. 40

Zhang et al Science 2007, 318 (16), 1121 DNA Reaction Networks A two-layer cascaded network. (A) Schematic. See table S 2 for sequences of new domains. (B) Kinetics. Indicated amounts of initial catalyst C 0 were added at t ≈ 0. Fluorescence derives from reporter complex OR (Fig. 1 D) at 30 n. M. Dotted lines show simulated traces; see SOM text S 8 for details on reaction rates and modeling. a. u. , arbitrary units. (Inset) Response to 0. 0010×, 0. 0003×, and 0. 0001× catalyst. The asterisk indicates that three independent reaction traces are shown. 1. 0 fluorescence units correspond to ≈ 10 n. M of triggered reporter. 41

Allosteric enzymes are enzymes that change their conformational ensemble upon binding of an effector, resulting in a change in binding affinity at a different ligand binding site. This provides "action at a distance" through binding of one ligand affet: ng the binding of another at a distant site. 42

Allosteric Enzymes 43 http: //resources. schoolscience. co. uk/unilever/16 -18/proteins/protch 6 pg 5. html

Allosteric DNA Catalytic Reactions D. Y. Zhang et al. JACS 2008, 130, 13921 44

Allosteric DNA Catalytic Reactions 45 D. Y. Zhang et al. JACS 2008, 130, 13921

Allosteric DNA Catalytic Reactions D. Y. Zhang et al. JACS 2008, 130, 13921 46

Allosteric DNA Catalytic Reactions 10 bp 44 bp 3 x 10^3 /s 1. 54 x 10^-5 /s 2 x 10^5 /M/s 22 bp 3 x 10^4 /M/s 14 bp D. Y. Zhang et al. JACS 2008, 130, 13921 30 bp 16 bp 47