Assembly of Dynamic Gated and Cascaded Transient DNAzyme Networks

The dynamic transient formation and depletion of G-quadruplexes regulate gene replication and transcription. This process was found to be related to various diseases such as cancer and premature aging. We report on the engineering of nucleic acid modules revealing dynamic, transient assembly and disassembly of G-quadruplex structures and G-quadruplex-based DNAzymes, gated transient processes, and cascaded dynamic transient reactions that involve G-quadruplex and DNAzyme structures. The dynamic transient processes are driven by functional DNA reaction modules activated by a fuel strand and guided toward dissipative operation by a nicking enzyme (Nt.BbvCI). The dynamic networks were further characterized by computational simulation of the experiments using kinetic models, allowing us to predict the dynamic performance of the networks under different auxiliary conditions applied to the systems. The systems reported herein could provide functional DNA machineries for the spatiotemporal control of G-quadruplex structures perturbing gene expression and thus provide a therapeutic means for related emergent diseases.


INTRODUCTION
Different biological processes such as cell proliferation, 1,2 cell motility, 3,4 and signal promotion 5 represent spatiotemporal reactions proceeding under dissipative, out-of-equilibrium conditions. Substantial recent research efforts are directed toward the development of synthetic systems emulating such processes. For example, the GTP-driven growth and division of protein fibrils in coacervated droplets was suggested as a model system mimicking spatiotemporal cell division. 6 Also, the dissipative carbodiimide-fueled synthesis of anhydrides 7 and the transient assembly and disassembly of fibers by the catalyzed hydrolysis of peptides 8 were demonstrated in systems operating out-of-equilibrium.
Within these efforts, the information encoded in nucleic acids provides versatile means to assemble spatiotemporal reaction networks and circuitries. The possibilities to control duplex strand displacement processes by fuel/antifuel strands dictated by the stability of the duplexes, 9,10 the reconfiguration of triplex nucleic acids through strand displacement or auxiliary triggers, 11 e.g., pH, the use of photoisomerizable intercalators, such as trans/cis-azobenzene, to assemble/disassemble nucleic acid duplexes, 12−14 and the many available enzymes to cleave or ligate nucleic acids, such as endonucleases, 15,16 nickases, 17 exonucleases, 18,19 DNAase, 20 ligase, 21−23 or biocatalytic nucleic acids (DNAzymes), 24−28 provide a rich arsenal of functional reconfiguration motives. Besides using these molecular tools to design DNA-based switches 29 and machines, 30−35 dynamic networks and circuitries, such as a synthetic transcriptional clock, 36 transcriptional oscillators, 37 bistable transcriptional switches, 38 and transcriptional regulatory networks 39 were demonstrated. Also, wired small DNA templates were cascaded to yield dynamically controlled oscillatory outputs, 40 and the dynamic out-of-equilibrium operations of such systems have been suggested to mimic natural ecosystems. 41 In particular, DNA reaction modules operating transient, out-of-equilibrium, processes were recently developed. For example, the formation of a ligand-aptamer complex, e.g., the AMP-aptamer complex, and its subsequent biocatalytic separation resulted in the assembly and dynamic depletion of an aptamer-ligand complex as a reaction intermediate. 42 In addition, different enzymes such as endonucleases, 43 nicking enzymes, 44 or synthetic catalytic nucleic acids, DNAzymes, 45 were applied as catalysts to control the dynamic transient reconfiguration of DNA networks that stimulate the assembly and dissipative depletion of DNA structures. Biocatalytically driven gated transient systems and dissipative cascades 44 were demonstrated, and the ATP-fueled transient ligation of DNAzyme subunits to yield catalytic DNAzymes was reported. 46 In addition, the biocatalytically driven transient reconfiguration of constitutional dynamic networks was reported, 47 and a dynamic transient feedback driven DNA network effecting the synthesis of oligonucleotides was coupled to giant membrane vesicles, thus acting as a protocell. 48 The triggered formation and dissipation of the biopolymer intermediate demonstrated signal-responsive adaptive properties of the protocell, mimicking cellular homeostasis. Different applications of transient DNA networks were suggested, such as the temporary uptake and release of loads 49,50 and the transient control over the optical properties of nucleic acid functionalized Au nanoparticles, semiconductor quantum dots or metal nanoclusters through their transient aggregation and disaggregation. 51 G-quadruplexes attract substantial research interest as functional reconfigurable nucleic acid based structures. DNA switches 52−55 and machines 56−60 relying on the reconfiguration of G-quadruplexes and the switchable catalytic activities of hemin/G-quadruplex DNAzymes, 61 have been a subject of extensive research. Different applications of reconfigurable Gquadruplex nanostructures were addressed including their use as reversible gating units of drug-loaded carriers, 62,63 functional units controlling the stiffness of hydrogel matrices for shapememory and controlled drug release, 64,65 and the selforganization of photodynamic therapeutic agents. 66,67 The dynamic transient formation and depletion of G-quadruplexes regulate the replication and transcription of genes, 68−73 and the dynamic folding of G-quadruplexes was found to be important in the telomerase-stimulated synthesis of telomeres. 74 Indeed, perturbing the folding and unfolding dynamics of G-quadruplexes was found to be related to various human diseases caused by genomic instability, such as premature aging and cancer. 75 Realizing that G-quadruplexes are unfolded in nature by helicase and that helicase efficiency could affect the spatiotemporal formation and disassembly of G-quadruplexes leading to these respective biological disorders, the development of synthetic dynamic routes to form and unwind G-quadruplexes could provide a therapeutic means for G-quadruplex-related diseases.
In the present study, we introduce nucleic acid systems demonstrating the dynamic transient assembly/disassembly and operation of G-quadruplex structures. We discuss means to control the dynamic processes by auxiliary stimuli, such as the concentrations of the triggering stimuli and the accompanying biocatalysts and strategies to guide the dynamic transitions of the systems by controlling the effects of inhibitors on the gating of the process. In particular, we demonstrate the integration of the dynamic reconfiguration of the G-quadruplex within a cascaded transformation involving information transfer and dynamic intercommunication between two dissipative transient systems. Figure 1A depicts the transient assembly of a hemin/Gquadruplex DNAzyme structure. The reaction module, state I, includes two duplexes, L 1 /T 1 and G 1 /C 1 , and nicking enzyme Nt.BbvCI, which acts as catalyst that controls the transient dissipative process. Hemin is added as an auxiliary effector to the reaction module. The strand G 1 in the duplex G 1 /C 1 consists of a guanosine-rich sequence that under appropriate conditions can assemble into a G-quadruplex. Subjecting the reaction module to trigger L 1 ′ displaces duplex L 1 /T 1 to yield duplex L 1 /L 1 ′. The released strand T 1 displaces duplex G 1 /C 1 to yield duplex T 1 /C 1 while releasing the strand G 1 that assembles in the presence of K + ions and hemin into the hemin/G-quadruplex DNAzyme. Duplex L 1 /L 1 ′ is engineered to be cleaved by nicking enzyme Nt.BbvCI resulting in the cleavage of L 1 ′ and the separation of L 1 . The released strand L 1 then displaces duplex T 1 /C 1 , releasing C 1 which disassembles the G-quadruplex through duplex formation to regenerate the initial reaction module, state I. Thus, the dynamic events proceeding in the network lead to the transient assembly and dissipative depletion of the hemin/G-quadruplex DNAzyme. The hemin/G-quadruplex DNAzyme catalyzed oxidation of 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) (ABTS 2− ) to the colored ABTS •− (λ = 420 nm) in the presence of hydrogen peroxide (H 2 O 2 ), provides a readout signal for the transient formation and depletion of the DNAzyme. Figure 1B Figure 1A.

RESULTS AND DISCUSSION
Using an appropriate calibration curve, relating the timedependent absorbance changes of ABTS •− to known standard concentrations of the hemin/G-quadruplex DNAzyme, Figure  S1, the transient concentration changes of the hemin/Gquadruplex DNAzyme were derived ( Figure 1C, dots). A kinetics model that accounts for the different steps involved in the transient process was formulated ( Figure S2) and solved computationally to determine the rate constants that describe the experimental results. The best-fit curve overlaying the experimental result is shown in Figure 1C (curve a′). The derived computational rate constants are summarized in Table  S1. For a detailed description of the procedure for the computational simulations presented in the study, see the Supporting Information, page S6. The computationally simulated results are valuable to predict behavior of the system under different auxiliary experimental conditions. Realizing that the dynamic experiments shown in Figure 1C were obtained in the presence of L 1 ′ (4 μM) and Nt.BbvCI (0.046 μM), the derived transient behavior of the system at two concentrations of L 1 ′ (2 and 6 μM) and a constant concentration of Nt.BbvCI (0.046 μM) were displayed in curves b′ and c′ (Figure 1 D). The predicted dynamic behavior was then experimentally validated, as shown with dots in curves b and c. Similarly, Figure 1E depicts curve d′ that predicts the transient behavior of the system in the presence of a higher concentration of the nicking enzyme (0.069 μM) and L 1 ′ (4 μM), and the dots (curve d) represent the experimental validation of the predicted curve. (For the experimental raw data leading to the results displayed in Figure 1D,E, see Figure  S3.) Very good agreement between the predicted transient dynamic kinetics patterns of the systems at different auxiliary conditions and the experimental results is demonstrated, indicating the success of the computational modeling of the kinetics of the complex dynamic machinery. The formation and depletion of the G-quadruplex in the system was further supported by circular dichroism (CD) experiments (see Figure  S4 and the accompanying discussion). In addition, the transient operation of the system shown in Figure 1 was further supported by quantitative gel electrophoretic experiments following the transient depletion and recovery of constituents L 1 /T 1 and G 1 /C 1 (see Figure S5 and the accompanying discussion).
A second reaction module demonstrating the transient dynamic assembly of a supramolecular hemin/G-quadruplex, consisting of two G subunits, is depicted in Figure 2A. The reaction module in state II is composed of duplex L 2 /T 2 , hairpin structure G 2 , and single-strand G 3 as constituents, nicking enzyme Nt.BbvCI as the participating catalyst, and hemin as the DNAzyme cofactor. Strands G 2 and G 3 include guanosine-rich sequences (blue) that act as subunits that assemble, under appropriate conditions, into the hemin/Gquadruplex supramolecular DNAzyme. Subjecting the reaction module in state II to trigger strand L 2 ′ displaces duplex L 2 /T 2 to yield L 2 /L 2 ′, and the released strand, T 2 , opens hairpin G 2 while simultaneously bridging the strands G 2 /G 3 and promoting their self-assembly into the hemin/G-quadruplex DNAzyme. Duplex L 2 /L 2 ′ is, however, engineered to include the nicking site in strand L 2 ′ to be cleaved by Nt.BbvCI. Cleavage of L 2 ′ leads to the release of L 2 that displaces strand T 2 from supramolecular complex T 2 /G 2 +G 3 , leading to separation of the hemin/G-quadruplex DNAzyme and to the eventual recovery of the rest module in state II. Thus, the network displayed in Figure 2A leads to the dynamic, transient formation and depletion of the supramolecular hemin/Gquadruplex DNAzyme structure. The dynamic behavior of the system was probed by the DNAzyme-catalyzed oxidation of ABTS 2− to ABTS •− . Figure 2B depicts the time-dependent absorbance changes of ABTS •− generated by the dynamically formed hemin/G-quadruplex DNAzyme samples after different time intervals following the activation of the transient system. Using an appropriate calibration curve, relating the timedependent absorbance changes of ABTS •− to known concentrations of the supramolecular hemin/G-quadruplex ( Figure S6), the concentrations of the transiently formed and depleted DNAzyme complex T 2 /G 2 +G 3 were evaluated, Figure  2C (dotted profile). The full absorption spectra of ABTS •− generated after a fixed time interval of 100 s by the samples withdrawn at differed time intervals following the activation of the transient system are presented in Figure S7A. The full absorption spectra of ABTS •− generated after 100 s by known concentrations of the DNAzyme T 2 /G 2 +G 3 are presented in Figure S7B. The absorbance values at λ = 420 nm were used to derive a respective calibration curve ( Figure S7C), following which the absorbance values recorded for the transient samples at λ = 420 nm, ε = 36 000 /(M·cm) ( Figure S7A), enabled the derivation of the transient concentrations of T 2 /G 2 +G 3 generated in the transient system ( Figure S7D). The kinetic model corresponding to the transient scheme depicted in Figure 2A was formulated ( Figure S8). The computationally simulated kinetic curve is presented as the solid curve (red) overlaid on the experimental data, Figure 2C. The derived rate constants (Table S2) were then used to predict the behavior of the network at different auxiliary conditions, and the predicted results were experimentally validated (curves b/b′, c/c′, and d/ d′ in Figure 2D,E; the raw results are displayed in Figure S9). The formation and depletion of the supramolecular Gquadruplex in the system was further supported by CD experiments (see Figure S10 and the accompanying discussion). Additionally, the transient operation of the system was supported by quantitative gel electrophoretic experiments following the transient depletion and recovery of the constituents L 2 /T 2 , Figure S11 and the accompanying discussion.
The successful assembly of transient catalytic DNAzymes by reaction modules consisting of appropriately engineered nucleic acid subunits as constituents was then applied to design reaction modules enabling the assembly of other transient DNAzyme nanostructures. Figure 3(A) introduces a reaction module, state III, that allows the transient operation of a Mg 2+ -ion-dependent DNAzyme. The reaction module consists of duplex L 3 /T 3 , the added subunits M 1 , M 2 , and nicking enzyme Nt.BbvCI. Upon triggering the module consisting of state III with L 3 ′, the duplex L 3 /T 3 is displaced to yield the duplex L 3 /L 3 ′ and the released strand T 3 , bridges the constituents M 1 /M 2 to yield Mg 2+ -ion-dependent DNAzyme. Nicking the duplex L 3 /L 3 ′ cleaves L 3 ′ and the separated strand L 3 displaces the intermediate Mg 2+ -ion-  Figure 3B reflect the content of the catalytic Mg 2+ -ion-dependent DNAzyme. By applying an appropriate calibration curve corresponding to the rates of the fluorescence changes (λ em = 516 nm) of the cleaved substrate S 1 by different known standard concentrations of the DNAzyme (Figure S12), the transient concentrations of the formed and dissipated Mg 2+ -ion-dependent DNAzyme, T 3 / M 1 +M 2 were evaluated, Figure 3C dots. A kinetic model was formulated (Figures S13 and S14 and the accompanying discussion) for the dynamic scheme shown in Figure 3A, and the experimental results were simulated using the kinetic model to yield the best-fit curve, the solid red transient Figure  3C. The set of rate constants derived from the fitted curve are summarized in Table S3. As before, the derived rate constants and kinetic model were used to predict the behavior of the transient system, in the presence of variable concentrations of the trigger, L 3 ′ ( Figure 3D, curves b′ and c′), and the presence of variable concentrations of the nicking enzyme ( Figure 3E, curves d′ and e′). The predicted results were validated experimentally (dots b and c, Figure 3D) and dots d and e, Figure 3E; for the raw experimental curves, see Figure S15). Very good agreement between the computationally predicted transient and the experimental results is demonstrated.
The successful design of two reaction modules that guide the transient operation of two different DNAzymes was then applied to develop the gated operation of the two DNAzymes, Figure 4. The system, state Q, consists of a mixture of the two duplexes L 2 /T 2 and L 3 /T 3 , the G-quadruplex subunit constituents G 2 and G 3 , strands M 1 and M 2 , and the nicking enzyme catalyst, Nt.BbvCI. Subjecting this composite to triggers L 2 ′ and L 3 ′ simultaneously leads to the parallel, nongated, transient operation of the hemin/G-quadruplex DNAzyme, catalyzing the oxidation of ABTS 2− to ABTS •− by H 2 O 2 and the cleavage of the substrate S 1 , generating the fluorescence changes. The parallel transient operation of the hemin/G-quadruplex DNAzyme, T 2 /G 2 +G 3, and of Mg 2+ -iondependent DNAzyme, T 3 /M 1 +M 2 , are presented in Figure 5A (the time-dependent catalytic curves of the two DNAzymes at time intervals are shown in Figure S16). A kinetic model combing the two transient DNAzymes was formulated ( Figure  S17) for state Q. Using the set of rate constants (summarized in Table S4) which were derived from the fitted curves of the individual transient DNAzymes, Figure 2 and 3, the transient dissipative curves corresponding to the parallel nongated DNAzymes were predicted, curve a′ and b′, and these are in good agreement with the experimental results. In order to achieve gated operation of the system, strand M 2 was pre-engineered to include a toehold domain that could hybridize with inhibitor strand I M . Treatment of the system in state Q with inhibitor I M therefore yields the reaction module in state R where strand M 2 is blocked. The L 2 ′and L 3 ′-triggered separation of duplexes L 2 /T 2 and L 3 /T 3 leads to duplexes L 2 / L 2 ′ and L 3 /L 3 ′ and to separated strands T 2 and T 3 . While T 2 results in the formation of hemin/G-quadruplex DNAzyme as before, the T 3 -stimulated formation of Mg 2+ -ion-dependent DNAzyme is inhibited by the blocking strand. In turn, the nicking of strands L 2 ′ and L 3 ′ in duplexes L 2 /L 2 ′ and L 3 /L 3 ′, by Nt.BbvCI leads to the formation of free L 2 , L 3 that rehybridize with T 2 , T 3 to recover to the rest reaction module, state R. Thus, subjecting state R to triggers L 2 ′ and L 3 ′ leads to the gated activation of hemin/G-quadruplex DNAzyme, yet the operation of the Mg 2+ -ion-dependent DNAzyme does not occur. Figure 5B shows that in the presence of I M the gated transient operation of the hemin/G-quadruplex DNAzyme, T 2 /G 2 +G 3 , proceeds effectively, while the activity of Mg 2+ -iondependent DNAzyme, T 3 /M 1 +M 2 , is almost fully blocked. Similarly, treatment of the mixture in state Q with the inhibitor strand I G (pre-engineered to block strand G 2 ) results in the hybridization of I G with the single strand toehold sequence engineered into hairpin G 2 , yielding the reaction module in state S. Interacting the system in state S with the two triggers L 2 ′ and L 3 ′ leads to the gated operation of the transient Mg 2+ion-dependent DNAzyme, while the formation of the hemin/ G-quadruplex DNAzyme is inhibited, since T 2 can not unlock blocked hairpin structure G 2 . Figure 5C demonstrates that the activity of the hemin/G-quadruplex is almost fully blocked, while the transient activity of Mg 2+ -ion-dependent DNAzyme is switched on. Two kinetic models that account for the transient gated operation of the two DNAzymes in the presence of inhibitors I M and I G were respectively formulated (Figures S18 and S19). As these models include a set of rate constants that are involved in the transient operation of the individual DNAzymes, that were computationally derived and experimentally supported, we adopted this set of rate constants and integrated them into the comprehensive kinetic model of the gated DNAzymes that include all rate constants associated with the participation of the inhibitors in the dynamic process. The kinetic models were applied computationally to the experimental results of the gated transient operation of the two DNAzymes (solid curves overlaid on the experimental dots, Figure 5). The sets of rate constants corresponding to the set of reactions associated with the kinetic models are summarized in Tables S5 and S6. These sets of rate constants were used to predict the performance of the gated DNAzyme systems at auxiliary conditions that differ from those applied to derive Figure 5. The predicted results at different auxiliary conditions and the experimental validation of the predicted results, are presented in Figures S20 and S21 and the accompanying discussion.
Besides the gated operation of the two transient DNAzymes, the cascaded operation of the two DNAzymes was achieved. Figure 6 depicts the scheme developed to intercommunicate between two reaction modules that allows the Nt.BbvCIcatalyzed operation of the DNAzyme cascade consisting of the hemin/G-quadruplex and Mg 2+ -ion-dependent DNAzymes. The system is composed of two reaction modules: modules I and II. Module I includes duplexes L 4 /T 4 and G 4 /C 4 and nicking enzyme Nt.BbvCI in its rest state. Module II includes duplex L 3 /T 3 , the subunits M 3 and M 4 and nicking enzyme Nt.BbvCI in its rest state. The triggered activation of module I by L 4 ′ displaces duplex L 4 /T 4 to yield L 4 /L 4 ′, and the released T 4 displaces duplex G 4 /C 4 to yield duplex T 4 /C 4 and to release strand G 4 that self-assembles into G-quadruplex-based DNAzyme 1. The nicking of strand L 4 ′ in duplex L 4 /L 4 ′ separate L 4 that displaces intermediate duplex T 4 /C 4 to yield energetically stabilized L 4 /T 4 , and the released C 4 acts as functional unit to separate G-quadruplex and regenerate the reaction module. That is, the L 4 ′-triggered dynamic operation of module I includes the machinery necessary to regenerate the rest of module I. Concomitant to this transient dynamic path, the transiently formed G-quadruplex product includes, however, the encoded information, i.e., extended single-strand tether y that acts as functional unit, to interact with module II and to activate the transient cascaded DNAzyme. In parallel to the dynamic process proceeding in module I, tether y, associated with the G-quadruplex, displaces duplex L 3 /T 3 associated with module II to yield duplex G 4 /L 3 and free strand T 3 . The released strand T 3 bridges subunits M 3 and M 4 to self-assemble the supramolecular Mg 2+ -ion-dependent DNAzyme that cleaves the fluorophore-quencher-modified substrate, S 1 . Tether y of G 4 , hybridized in duplex G 4 /L 3 , includes, however, the sequence to be nicked by Nt.BbvCI, and the cleavage of G 4 yields fragment G 4−2 and releases strand L 3 . The released strand L 3 displaces strand T 3 associated with Mg 2+ -ion-dependent DNAzyme, resulting in the dynamic transient separation of Mg 2+ -ion-dependent DNAzyme 2 and the regeneration of the rest state of module II. The released "waste" strand product, G 4−2 , generated upon the cleavage of duplex G 4 /L 3 includes, in its free tether, the engineered sequence x that includes the capacity to displace intermediate duplex T 4 Figure 7C, dots, curves a and b). A kinetic model that accounts for the transient cascaded DNAzyme system was formulated ( Figure  S23). This kinetic model includes a set of rate constants that are associated with the individual DNAzyme previously computationally and experimentally supported and add rate constants associated with the dynamic communication between the two cascaded reaction modules (Table S7). The integrated kinetic model was then applied to computationally fit the experimental transients of the DNAzymes participating in the two-enzymes cascade. The computational transient curves are overlaid on the experimental results (solid line curves a′ and b′, Figure 7C).

CONCLUSION
The study introduced synthetic systems driving the transient operation of G-quadruplexes, a dynamic gated system of transient DNAzymes, and a transient cascaded system of DNAzymes. Realizing the significance of dynamic formation and depletion of G-quadruplexes in controlling the replication and transcription of genes and the consequences of malfunctions of this process in causing diseases, the present study introduces synthetic modules to form and separate Gquadruplexes. In fact, substantial efforts are directed to develop methods to form and unwind G-quadruplexes 76,77 as therapeutic means to fight G-quadruplex related diseases. Metal ions, 78 complexes, 79,80 photoresponsive ligands, 81,82 and natural polyamines such as spermine 83 were used to control Gquadruplexes stability and topology. In this context, coupling functional DNA machineries to G-quadruplex structures as a means to dissipatively perturb G-quadruplex structures could provide a versatile path for the spatiotemporal regulation of Gquadruplexes. The different systems described in the study operated, however, in homogeneous buffer solutions. As future applications of such networks are envisaged for therapeutic applications, the use of the artificial networks in native bioenvironments is an important goal. Indeed, G-quadruplexes and Mg 2+ -ion-dependent DNAzymes were suggested as catalytic agents for cancer therapy. 84−86 Thus, toward the possible use of such artificial networks in native media, we examined the operation of the transient network displayed in Figure 2 in a cancer cell lysate. The results and the accompanying discussion are presented in Figure S24. We find that the transient system shown in Figure 2 successfully operates in the cell lysate, yet the cell lysate affects the dynamics of the transient process as compared to the pure buffer solution. We find that the activity of nicking enzyme Nt.BbvCI is lowered by ca. 25% in the cell lysate, and this results in a slightly elevated peak content of transient complex T 2 /G 2 +G 3 and a slower recovery of the parent reaction module. Nonetheless, the results indicate the feasibility to operate such artificial networks in native environments.

EXPERIMENTAL SECTION
Oligonucleotides. Oligonucleotides were purchased from Sigma-Aldrich and Integrated DNA Technologies, Inc. The following sequence strands (5′ → 3′) were used to construct the different systems: (1) G 1 , TTTGGGTAGGGCGGGTTGGG; (2) C 1 : CATCAATCCCAACCCGTCCTACC; (3) T 1 , TTTTTTT-TTTATAGGACGGGTTAGGATTGAT; (4) L 1 , TTTTTTTT-T C A A T C C T A G C T G A G G C C C G T C C T A T A ; ( 5 ) L 1 ′ , C G G G C C T C A G C T A G ; ( 6 ) G 2 , T A C A G C T C C -TAGTTTAGCCGCCATGGGTAGGGCGGG; (7)  Preparation and Measurement of Transient, Dissipative DNAzyme Systems. The composition and characterization of the different systems discussed in the paper are detailed in the Supporting Information. As an example, the composition and operation of the cascaded system presented in Figures 6 and 7 are described in brief below, and further details are presented in the Supporting Information. The cascaded system consisted of a mixture of T 4 /L 4 (2 μM), G 4 /C 4 (2 μM), T 3 /L 3 (1 μM), M 3 (1 μM), M 4 (1 μM), Nt.BbvCI (0.069 μM), and hemin (2 μM) in 1× rCutSmart Buffer, with a total volume of 1.0 mL. Upon adding trigger L 4 ′ (6 μM) to the mixture (0 h time point), the dissipative system was incubated at 33°C . For the measurement of the time-dependent absorbance changes of ABTS •− catalyzed by hemin/G-quadruplex DNAzyme in the cascaded system, 40 μL aliquots of the mixture were withdrawn at different time intervals. Each aliquot was mixed with 20 μL of ABTS 2− (1 mM) and 20 μL of H 2 O 2 (1 mM) in a quartz cuvette with 10 mm path length. The time-dependent absorbance changes of ABTS •− at 420 nm (ε = 36 000/M·cm) were recorded at 25°C on a UV-2450 spectrophotometer (Shimadzu). For the measurement of the timedependent fluorescence changes of the cleavage of S 1 catalyzed by Mg 2+ -ion-dependent DNAzyme in the cascaded system, aliquots of 50 μL were withdrawn at different time intervals and treated with 50 μL of S 1 (2 μM, supplemented with 10 mM Mg 2+ ). The time-dependent fluorescence changes (λ ex = 496 nm, λ em = 516 nm) of S 1 were monitored using a plastic cuvette with 10 mm path length at 25°C on a Cary Eclipse Fluorometer (Varian, Inc.).

* sı Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsnano.1c11631. Chemicals, preparation of different transient DNAzyme systems, measurement methods, characterizations, calibration curves corresponding to the analyses of different systems, CD spectra, gel electrophoresis, time-dependent absorbance changes of ABTS •− , absorbance spectra of ABTS •− , fluorescence changes of the cleaved S 1 at different time intervals of transient DNAzyme systems, computational kinetic models for simulations, tables summarizing the rate constants corresponding to different systems, cell lysate experiment (PDF)