Programmable dynamic steady states in ATP-driven nonequilibrium DNA systems

Chemical fuel and reaction networks program nonequilibrium steady-state structural dynamics in dynamic covalent DNA systems.

. Oligonucleotide sequences. Fig. S1. Hybridization of the self-complementary ends of the DNA monomer strands M 1 in dependence of temperature and ligation reaction catalyzed by T4 DNA ligase.    Restriction kinetics of the DNA chain cleavage reaction as a function of BamHI concentration. First, the DNA substrate of the enzymatic digestion assay of BamHI was prepared by ligation of the monomer fragment, M 1 , to maximum conversion into long DNA chains. The ligation reaction was typically assembled in a total volume of 50 µl by sequential addition of water, hybridized DNA (M 1 , 0.1 mM), 10x buffer E (1x dilution), BSA (0.1 g/L) and T4 DNA ligase (50 WU, 1 WU/µl). The solution was mixed gently by pipetting up and down and centrifuged shortly before addition of the ATP (1 mM) to initiate the ligation reaction. The ligation reaction was incubated in a thermoshaker at 25 °C and 250 rpm for 24 h and subsequently the T4 DNA ligase was heat-deactivated at 70 °C for 10 min. Several substrate batches of the ligated DNA chains were combined and carefully mixed to ensure the same starting material for every restriction assay. The kinetic assays of the cleavage reaction were assembled in a total volume of 90 µl by sequential addition of water, ligated DNA substrate (equivalent to 0.05 mM M 1 ), 10x buffer E (1x dilution) and BSA (0.1 g/L). The solution was mixed gently by pipetting up and down and centrifuged shortly before addition of the BamHI restriction enzyme to start the cleavage reaction. The concentration of the BamHI restriction enzyme varied from 450 U (5 U/µl) to 1800 U (20 U/µl). The enzymatic restriction reaction was incubated in a thermoshaker at 25 °C and 250 rpm and kinetic aliquots (6 µl) were taken at predetermined time intervals. These aliquots were treated and analyzed according to the Time-dependent aliquots (6 µl) were withdrawn from the reaction tube and immediately quenched in quenching buffer containing EDTA and subsequent freezing in liquid nitrogen. Kinetic aliquots were analyzed by GE in 2 wt% agarose gels in TAE buffer, 90 V = const., 300 mA, 2.5 h. The gel was analyzed by selective fluorophore imaging. The fluorescein-labeled DNA was imaged with excitation using a blue LED (ca. 465-475 nm) and a band-pass filter centered at 545 nm (BP 40 nm), while excitation with a red LED (ca. 620-630 nm) and a band-pass filter at 690 nm (40 nm) was used for the Cy5-labeled DNA. The DNA molecular weight ladders were visualized using the blue LED and a band-pass filter at 605 nm (50 nm) after post-staining with SYBR gold. The gel images were stacked and processed in ImageJ, including correction of background, brightness, contrast and coloring, to obtain a multi-color composite image of both dyes, and further analyzed by gray scale profiling. See Fig. 4F in the main manuscript.
Enzymatic cleavage of the FRET duplex (F) with BamHI. In a typical cleavage reaction, the hybridized FRET duplex F (25 µM) was incubated with BSA (0.1 g/L) and the restriction enzyme BamHI (8 U/µl) in 1x buffer E at 37 °C, 300 rpm for 48 h.

Refueling of dynamic FRET duplex ligation by multiple additions of ATP.
Multiple repetitions of the transient, dynamic ligation of the FRET duplex (= dynamic covalent bond formation) were carried out in a total volume of 200 µl. The reaction solution was assembled by sequential addition of water, the cleaved fragments of the FRET duplex F (1 µM), 10x buffer E (1x dilution), BSA (0.2 g/L) and mixed gently by pipetting up and down. The overall glycerol content was typically kept at 5 vol%. The solution was transferred into a quartz glass cuvette (d = 3 mm) and equilibrated at 25 °C in the holder of the fluorescence spectrometer. The enzymes, BamHI (100 U) and T4 DNA ligase (4.58 WU), were added after 5 min. After another 5 min of equilibration, the reaction was started by addition of ATP (2 µM

Supplementary Note A. Development of the conditions for the dynamic reaction network by characterization of the individual enzyme reactions
Both the T4 DNA ligase and the BamHI restriction enzyme-catalyzed reactions were characterized independently of each other with the DNA monomer M 1 and its ligated polymer as substrates to establish suitable reaction conditions for the ATP-fueled dynamic polymerization system. We analyze different reaction parameters, involving the influence of enzyme, DNA and ATP concentration, reaction time and temperature, and enzyme stability, and discuss their effect on a step-growth-like polymerization in the following. Methodological details on GE analysis are provided in Supplementary Note B.

Hybridization Efficiency and Melting Behavior of the Self-Complementary Ends of Monomer Strand M 1
The transient DySS polymerization is conditional on the fact that the monomers may only polymerize in dependence of energy input via a chemically fueled reaction. Therefore, the selfcomplementary ends, which serve as telechelic end groups of the DNA monomer strands, M 1 , are intentionally kept short to prevent uncontrolled self-hybridization and elongation into polymer chains ( fig. S1A, B). The NUPACK(40) prediction of the melting profile of the 4 bp DNA hybridization (GATC) underpins that the self-complementary ends are largely unpaired under our reaction conditions (16 -37 °C). Figure S1C describes the ATP-dependent ligation reaction in general terms and fig. S1D shows greater mechanistic details of the enzyme-catalyzed phosphodiester bond formation. With regard to later stoichiometry and energy considerations, it is important to note that complete joining of the ssDNA overhangs of two DNA monomers consumes two molecules of ATP because of nick sealing in both strands of the duplex. Note that the fuel is not incorporated into the final structure, but only mediates bond formation as energy source. This provides important flexibility in the design of partners to be joined. The predicted melting profile of this 4 bp hybridization shows that the bases are largely unpaired over the whole temperature range from 0 °C to 45 °C (conditions similar to a typical polymerization system: 0.05 mM DNA, 100 mM Na + and 6 mM Mg 2+ ). (C) Ligation reaction of two DNA monomer strands M 1 as seen in our step growth reaction of DNA chains. Covalent coupling of two monomer strands consumes two molecules of ATP as the formation of a phosphodiester bond in each single strand is catalyzed by an ATP-dependent T4 DNA ligase reaction. (D) Three-step reaction mechanism of T4 DNA ligase catalyzing the formation of a phosphodiester bond between the adjacent 3'-hydroxyl and 5'-phosphate group in a nicked DNA duplex.

Definition of Activity Units of both Enzymes
Definition of the Weiss Unit to describe the activity of T4 DNA ligase (Promega): 0.01 Weiss Unit [WU] of T4 DNA Ligase is the amount of enzyme required to catalyze the ligation of greater than 95% of 1 μg of λ/HindIII fragments at 16 °C in 20 minutes. Unit definition to describe the activity of BamHI (Promega): One Unit [U] is defined as the amount of enzyme required to completely digest 1 µg of lambda DNA in one hour at 37 °C in 50 µl assay buffer containing acetylated BSA added to a final concentration of 0.1 g/L.

Ligation Kinetics of the DNA Chain Growth in Dependence of T4 DNA Ligase
The kinetics of the T4 DNA ligase-catalyzed polymerization of the M 1 monomer strands (0.05 mM) were analyzed at 25 °C. Variation of the enzyme concentration from 5.5 WU to 110 WU increases the turnover in the system, which leads to faster built-up of the polymer chains until a constant plateau is reached ( fig. S2H). All ligation experiments were carried out with an excess of 1 mM ATP to exclude any conversion-related limitations of this step-growth polymerization.

Ligation Kinetics of the DNA Chain Growth in Dependence of ATP
Due to the step-growth character of the ATP-dependent T4 DNA ligase-catalyzed polymerization of the DNA monomer M 1 , the amount of supplied ATP can be used to purposely limit the conversion, and, thus, the degree of polymerization (= average chain length) of the M 1based DNA polymers. A substoichiometric amount of ATP compared to the theoretical number of ligation sites (= 2x monomer concentration) reduces the average chain length of the DNA polymer chains drastically ( fig. S3A-D). High molecular weights can only be reached at high conversions, which require at least equimolar amounts of ATP ( fig. S3E,F).

Long-Term Development of T4 DNA Ligase-Catalyzed DNA Chain Growth and Time-Dependent Activity Assay of the T4 DNA Ligase
The maximum molecular weight attainable for the M 1 -based DNA polymers is given by the extent of the step growth reaction. A T4 DNA ligase-catalyzed polymerization reaction (standard conditions: 25 °C, 0.05 mM M 1 , 41.25 WU T4 DNA ligase and excess 1 mM ATP) was carried out over a continued period of nine days to monitor how quickly maximum conversion is obtained. fig. S4A,B displays a rapid growth of the DNA chains, which already levels off after the first hours and stays constant thereafter at around ̅̅̅ w = 1200 bp. This excludes reduction of the average chain lengths due to time-limited conversion. However, given the complex nature of the system, the maximum chain lengths of the polymerization system may also be affected by slight batch-to-batch variations in reactant quality (e.g. enzyme activity, DNA purity and end group functionalization). To ensure comparability and reproducibility, all measurements within one experimental series of the kinetic studies were carried out using the same batches of reactants (DNA, enzymes, ATP).
The stability of the T4 DNA ligase over prolonged periods of time is of utmost importance for enabling the ATP-fueled transient DySS polymerization system, as it ensures the continuous energy input into the system via conversion of ATP and because it maintains the dynamic nonequilibrium steady-state character of the dynamic covalent system with continuous joining of phosphodiester bonds. The time-dependent T4 DNA ligase activity was assayed by short test ligation reactions (30 min reaction time). To this end, the DNA monomer fragment M 1 was incubated with T4 DNA ligase in a reaction tube under the standard reaction conditions at 25 °C (without ATP). Aliquots were taken on a daily basis and supplemented with fresh ATP to test for ligation efficiency. fig. S4C,D demonstrates that the obtained average chain length ̅̅̅ w of the polymer chains stays fairly constant over the investigated experimental time frame of 12 days. Minor decreases of enzyme activity do not interfere with the overall integrity of the DySS polymerization system.

Restriction Kinetics of the DNA Chain Degradation in Dependence of BamHI
An understanding of the time scales of the DNA cleavage in comparison to the ligation is critical to set up a suitable concentration ratio between the antagonistic enzymes, that fulfills the kinetic boundary condition for generating a transient system with faster activation than deactivation. We analyzed the restriction kinetics of BamHI, independently of the T4 DNA ligase, using previously ligated and heat-deactivated M 1 -based DNA polymers P 1 as substrate. Increasing amounts of BamHI (450 U to 1800 U) strongly accelerate the digestion reaction to the original monomer M 1 . The speed of the digestions scales with the BamHI concentration. Full digestion of P 1 takes up to four days for all BamHI concentrations and is hence much slower than the ligation reaction (see fig. S2). This enables the kinetic condition necessary in a non-equilibrium DySS polymerization.

Supplementary Note B. Routine of GE analysis: From the agarose gel to an average chain length
The enzyme-catalyzed step growth reaction of the DNA monomer, M 1 , leads to a distribution of DNA chains with a broad range of molecular weights (38 bp to > 10000 bp). GE allows separation of DNA chains with molecular resolution down to a few base pairs (bp). Band resolution scales mainly with the agarose concentration (i.e. effective pore size of the gel), applied voltage and run time. GE conditions were optimized in TAE buffer to satisfy imaging of the broad chain length distribution. We chose an agarose concentration of 2 wt% (90 V, 90 min) to identify clearly the number of single repeat units of the oligomers (monomer, dimer, trimer, …) as illustrated in fig. S6A. Band resolution gets poorer, i.e. molecular weight separation is less resolved, for longer DNA chains, which effectively cuts down the tail of the molecular weight distribution and reduces the measured average chain length and dispersity. DNA staining is based on Roti-GelStain, a benzimidazole dye binding to the minor groove of the DNA double helix. The binding scales with the length of the DNA duplex. Thus, the fluorescence signal obtained from the DNA staining is proportional to the DNA concentration and chain length (its mass), and the extracted gray scale profile from each lane of the agarose GE images corresponds to a mass-weighted chain length distribution. DNA base pair ladders allow a calibration of the GE images and calculation of an average chain length as demonstrated below. The GE images of the kinetic electrophoretic mobility shift assays were routinely analyzed to obtain quantitative data on the development of the average chain length over time. The procedure is shown in fig. S6

Equation 2
This fit function is used to recalculate the gray scale profiles as a function of base pair number. The band position of the monomer strand is normalized to its length of 38 bp ( fig. S6E). From this chain length distribution, the mass average chain length ̅̅̅ is obtained via applying Eq. 3 with bp i as the base pair number of fraction i and f i as the intensity value of fluorescence intensity of the corresponding fraction i.
Equation 3 The average DNA chain length ̅̅̅ is plotted over time to estimate the temporal evolution of the enzymatic polymerization reaction ( fig. S6F). The FRET duplex F with the fluorescent tags Cy3 and Cy5 next to the restriction/ligation site can be cleaved by BamHI and religated by T4 DNA ligase completely without any residual traces as seen by the single DNA bands in GE. Lane assignment: 1: original FRET duplex, 2: cleaved state, 3: religated state. (B) Corresponding fluorescence spectra normalized to the Cy3 donor emission peak at 571 nm. The religated FRET duplexes show 1/3 of the original FRET emission at 674 nm (Cy5 acceptor) due to statistic recombination of the cleaved DNA duplex fragments F Cy3 and F Cy5 to F Cy3 F Cy3 , F Cy5 F Cy5 and F Cy3 F Cy5 (1:1:1). Critically, only F Cy3 F Cy5 induces FRET. (C) Schematic representation of the different FRET duplex bonding states. (D) Fluorescence spectra during cleavage of the original FRET duplex F with 100 U BamHI, and (E) evaluation of the Cy3 donor emission at 571 nm (green dot), the Cy5 acceptor emission at 674 nm (red triangle) and the FRET ratio (674 nm/571 nm, black squares) over time. (F) Religation kinetics of the cleaved FRET duplex fragments (F Cy3 , F Cy5 ) with 4.58 WU and 4 µM ATP as represented by the time-dependent fluorescence signals of the Cy3 donor at 571 nm (green dot), the Cy5 acceptor at 674 nm (red triangle) and the FRET ratio (674 nm/571 nm, black squares). All fluorescence spectra were recorded in 1x buffer E with 1 µM F, 0.2 g/L BSA, λ exc. = 505 nm, 1 s integration time, 25 °C.
The original FRET duplex F hybridized from strand F a and F b shows a maximum FRET emission at 674 nm (= 100 %, black line, fig. S10B), because all Cy3 donors are positioned next to their Cy5 acceptor FRET partners. After complete enzymatic cleavage with BamHI, both dyes are fully separated into two duplex fragments (F Cy3 and F Cy5 , both 21 bp in length) with no FRET being observed (= 0 %, red line, fig. S10B). Upon religation of these cleaved duplex fragments by T4 DNA ligase the maximum FRET emission does not and cannot recover to the original value. This is due to a statistic recombination of the palindromic (self-complimentary) ends of the cleaved parts. Religation of the cleaved DNA duplex fragments F Cy3 and F Cy5 leads to F Cy3 F Cy3 , F Cy5 F Cy5 and F Cy3 F Cy5 in a 1:1:1 ratio. Critically, only F Cy3 F Cy5 shows FRET. The possible reaction products upon religation are illustrated in fig. S10C. Hence, the FRET efficiency is reduced to 1/3 (= 33 %, blue line) of the original state. Ultimately, the fully cleaved and religated state represent the limiting cases of the dynamic DNA bond formation, and, thus, the accessible and tunable range of the fluorescence spectra changes due to FRET in the DySS experiments presented in the manuscript ( Figure 4) and Section 1.11. Figure S10D-F show the spectral changes during cleavage of F and of the religation of F Cy3 and F Cy5 . Enzymatic cleavage of the FRET duplex reduces the FRET-induced emission of the Cy5 acceptor at 674 nm and strengthens the Cy3 donor emission at 571 nm ( fig. S10D,E). The opposite behavior is observed for the ligation reaction on the cleaved DNA by reformation of the FRET pair (however to a lesser extent due to statistical intermixing). In the following, the FRET ratio (Cy5/Cy3 = I 674 nm /I 571 nm ) is used for the time-resolved evaluation of the dynamic bonding state of the FRET duplex and converted to a relative percentage of ligation using the accessible FRET signal limits of the DySS. Ultimately, this relative degree of bonding translates into an ensemble average steady-state bond strength of the dynamic system. We observed that the presence of the DNA-bound enzymes slightly lowers the FRET efficiency between the Cy3/Cy5 pair.

ATP-Dependent Temporal Control of the Dynamic DNA Bond Visualized by Time-Dependent FRET
The average lifetime of the dynamic covalent DNA bond, as represented here by the dynamic transient ligation of the FRET duplex fragments, F Cy3 and F Cy5 , can be controlled by the amount of ATP as chemical fuel. Increasing amounts of ATP elongate the DySS phase by several hours under the chosen conditions ( fig. S11A,B). Transient dynamic ligation can be reactivated multiple times when supplemented with new ATP (fig. S11C).