Design and Analysis of Linear Cascade DNA Hybridization Chain Reactions. Using DNA Hairpins. Reif 1. Duke University. Durham, NC 27708, USA

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1 Design and Analysis of inear Cascade DNA Hybridization Chain eactions Using DNA Hairpins Hieu Bui, Sudhanshu Garg, Vincent Miao, Tianqi Song, eem Mokhtar, John eif Department of mputer Science, Department of Biomedical Engineering, Duke University Durham, NC 7708, USA Supporting Information

2 S: Sequence Design via NUPACK In general, the design process begins with a set of target DNA nanostructures consisting of 9 hairpins and initiators. Each hairpin structure has a - bp stem, 8- nt loop, and 6- nt external toehold. Hairpin 9 has a slightly longer loop length of - nt. In order to displace the stem domain and form a thermodynamically stable structure, each target molecule forms a - bp duplex with a designated hairpin strand. The melting temperature of a - bp duplex is estimated to be 55 to 65 o C at.5 mm Mg + salt concentration and ph 8.0. The reporter complex consists of a 0- bp duplex with 7- nt toehold. All binding domains are assigned with nucleotides using three letter codes (A, T, C) in order to minimize downstream undesirable leaks. NUPACK has built- in functions to ) accommodate sequence symmetry minimization, ) find the average number of incorrect nucleotides relative to target structures at equilibrium, ) generate the probability map of adopting target structures at equilibrium, and ) apply DNA hybridization kinetics. A set of stringent stopping conditions ensures a higher probability of obtaining desirable target structures; however, it takes longer to generate such structures. In our system, a list of stopping conditions includes ) target initiator structures cannot form undesirable complexes with more than 5% of all generated structures, ) target structures cannot have more than three consecutive guanine bases or more than four consecutive bases of any other nucleotide. The number of trials is set to 0, which means that there are 0 different matching sets of target molecules from the given specification list. The actual

3 sequence composition can be assigned or unassigned. Since we adopted the same reporter complex reported by Zhang et al., the sequences for the reporter complex are known. As a result, a portion of binding domains in the linear cascade reaction share the same sequences as the reporter complex. The script to generate target DNA sequences for our system is shown below:

4 design an HC system of 9 distinct hairpins design material, temperature (C), and trials material = dna temperature = 5 trials = 0 magnesium = 0.05 sodium = 0.5 target structures structure hairpin = D U8 U6 structure hairpin = U6 D U8 structure hairpin = D U8 U6 structure hairpin = U6 D U8 structure hairpin5 = D U8 U6 structure hairpin6 = U6 D U8 structure hairpin7 = D U8 U6 structure hairpin8 = U6 D U8 structure hairpin9 = D U U6 structure initiator = U structure initiator = U structure initiator = U structure initiator = U structure initiator5 = U structure initiator6 = U structure initiator7 = U structure initiator8 = U structure initiator9 = U structure C = D0 (+ U7) structure initiatorc = U sequence domains domain s0 = N6 domain s = TACCTA domain s = CTCTTT domain s = CCACCC domain s = CCTCCT domain s5 = TCTTTC domain s6 = TCTTCC domain s7 = TTTCCT domain s8 = CTTCTC domain s9 = T CATTC domain r = ACATACATCA domain l = T domain l = AA domain l = GC domain ci = N domain c0 = CCAC domain c = TTCT domain c = CATT domain c = CAAC domain c = ACTC domain c5 = ATCG domain c6 = TTTA domain c7 = CCAC domain c8 = CT CC domain c9 = TATTCCC domain t = CATTC AA domain bm = CC ACATACATCA TATTCCC T

5 thread sequence domains onto target structures hairpin.seq = c0 r c s l ci* r* c0* s0* hairpin.seq = s* c* r* c0* l s c r c hairpin.seq = c r c s l c* r* c* s* hairpin.seq = s* c* r* c* l s c r c hairpin5.seq = c r c5 s5 l c* r* c* s* hairpin6.seq = s5* c5* r* c* l s6 c6 r c5 hairpin7.seq = c6 r c7 s7 l c5* r* c6* s6* hairpin8.seq = s7* c7* r* c6* l s8 c8 r c7 hairpin9.seq = c8 r c9 s9 l l c7* r* c8* s8* initiator.seq = s0 c0 r ci initiator.seq = c0 r c s initiator.seq = s c r c initiator.seq = c r c s initiator5.seq = s c r c initiator6.seq = c r c5 s5 initiator7.seq = s6 c6 r c5 initiator8.seq = c6 r c7 s7 initiator9.seq = s8 c8 r c7 initiatorc.seq = c8 r c9 s9 l l C.seq = bm t* bm* specify stop conditions for normalized ensemble defect default:.0 (percent) for each target structure initiator.stop = 5.0 larger defect for unpaired structures prevent = SSSS, AAAAA, AAAA, GGG Script : NUPACK code to generate designed C system S: Modeling the reaction kinetics of linear cascade DNA hybridization reactions via chemical reaction equations Each DNA hairpin in the proposed system is treated abstractly as an individual molecule and is assumed to only bind the designated DNA strand strictly via DNA hybridization and strand displacement thermodynamics. The rates of all the reactions in 9 hairpins system can be described based on the second order kinetic process. 5

6 I + H!! P () P + H!! P () P + H!! P () P + H!! P () P + H5!! P5 (5) P5 + H6!! P6 (6) P6 + H7!! P7 (7) P7 + H8!! P8 (8) P8 + H9!! P9 (9) P9 + C!! FQ + TET (0) We further assume that the reverse reaction is negligible, although it is possible in autocatalytic DNA systems reported by Zhang et al.[9]. Since the number of base pairs from each cascade reaction is equal, we assume the forward rate constants are relatively equivalent for reactions () to (9). For the rate constant from the reaction (0), we used the same rate constant reported by Zhang et al.[9]. 6

7 ncentration (nm) hairpin (x I) hairpins (x I) hairpins (x I) 6 hairpins (x I) 9 hairpins (x I) ncentration (nm) hairpin (x I) hairpins (x I) hairpins (x I) 6 hairpins (x I) 9 hairpins (x I) Time (minutes) Time (minutes) ncentration (nm) hairpin (x I) hairpins (x I) hairpins (x I) 6 hairpins (x I) 9 hairpins (x I) ncentration (nm) hairpin (x I) hairpins (x I) hairpins (x I) 6 hairpins (x I) 9 hairpins (x I) Time (minutes) Time (minutes) Figure S: Modeling linear cascade DNA hybridization reactions with different rate constants (k) (i.e 0.5 x 0 5, 0 5, 5 x 0 5, 0 6 /M/s). The length of linear duplex is a function of the number of hairpins. Simulation analysis shows results from implementing different rate constants S: Matlab scripts The following scripts consist of two parts. Part one contains a function to solve the linear cascade DNA hybridization reaction involving nine distinct hairpins. Here, the function consists of a list of 0 bimolecular reactions as shown in Section S. Part two contains a function to ) simulate DNA hairpin interactions with the given initial concentrations and rate constants or ) optimize the least squares fit between the experimental data and 7

8 simulation data to determine the rate constant, in similar fashion to the previously reported method by Zhang et al. [7]. %%% This function is used to solve cascade chain reactions %%% Date: July, 06 function dy = lcr9(t,y) % % I + H -> IH ( + -> ) % % IH + H -> IH ( + 5 -> 6) % % IH + H -> IH ( > 8) % % IH + H -> IH ( > 0) % % IH + H5 -> IH5 (0 + -> ) % % IH5 + H6 -> IH6 ( + -> ) % % IH6 + H7 -> IH7 ( + 5 -> 6) % % IH7 + H8 -> IH8 ( > 8) % % IH8 + H9 -> IH9 ( > 0) % % IH9 + C -> OF (0 + -> ) dy = zeros(,); krep =.E6*60; % ate constant (/M/min) from earlier studies by Zhang et al. dy() = - y() * y() * y(); dy() = - y() * y() * y(); dy() = y() * y() * y() - y() * y() * y(5); dy(5) = - y() * y() * y(5); dy(6) = y() * y() * y(5) - y() * y(6) * y(7); dy(7) = - y() * y(6) * y(7); dy(8) = y() * y(6) * y(7) - y() * y(8) * y(9); dy(9) = - y() * y(8) * y(9); dy(0) = y() * y(8) * y(9) - y() * y(0) * y(); dy() = - y() * y(0) * y(); dy() = y() * y(0) * y() - y() * y() * y(); dy() = - y() * y() * y(); dy() = y() * y() * y() - y() * y() * y(5); dy(5) = - y() * y() * y(5); dy(6) = y() * y() * y(5) - y() * y(6) * y(7); dy(7) = - y() * y(6) * y(7); dy(8) = y() * y(6) * y(7) - y() * y(8) * y(9); dy(9) = - y() * y(8) * y(9); dy(0) = y() * y(8) * y(9) - krep * y(0) * y(); dy() = - krep * y(0) * y(); dy() = krep * y(0) * y(); return Script : C function to solve bimolecular cascade reactions 8

9 function err_fun = rate(input) data = load('path-to-data-file ); k = exp(input()); scalingconst = exp(input()); err_fun = 0; options = odeset('eltol', e-, 'AbsTol', e-0); datasize = size(data,); t = data(:datasize,); y0=5e-9*[,, 0,, 0,, 0,, 0,, 0,, 0,, 0,, 0,, 0,., 0]; % initial concentrations [t y]=odes(@lcr9, t, [k, y0], options); % 9H %%% find minimum error between the ODE solution and data ye = y(:,size(y,)) * scalingconst + data(,); for i = :size(data,) err_fun = err_fun + (ye(i) - data(i,))^/ye(i); end return % Fitting the experimental data using the least squares method by calling the err_fun function. The err_fun function then uses the lcr9 function to solve the ODE with the given initial conditions. clear all close all % Use this one to figure out the rate k0 = log(e6*60); % initial guess scale0 = log(e); % initial guess [k, fval] = fminunc(@rate,[k0, scale0]); Script : Error function to determine the rate constant. 9

10 So C8 S9 C8 S9 Hairpin 9 H 9 Initiator I C complex Schematic B So So So C8 C0 C S C C0 S S9 Hairpin 9 H 9 Initiator I C C S Hairpin I H S9 So So S C8 C7 C8 S8 Hairpin 8 H 8 C complex C C C C S Hairpin H S8 C8 C6 S C C (A) C7 C7 S7 Hairpin 7 H 7 S7 C7 C5 C6 C6 S6 S6 C6 C C5 C5 S5 S5 C5 C C C S C C S Hairpin H Hairpin 6 H 6 Hairpin 5 H 5 Hairpin H Schematic C Figure S: Estimation of yield via maximum fluorescence intensity readout. All experimental data were collected at 5 nm concentration. Assume that the maximum fluorescence intensity at thermal equilibrium is correlated with the yield of hairpins participating in the linear cascade reaction. Black curve is the fluorescence emission of initiating the last hairpin and resulting in displacing the reporter complex (schematic B). Cyan curve is the fluorescence emission of initiating the first hairpin and resulting in displacing the reporter complex after the linear cascade reaction (schematic C). The maximum fluorescence at thermal equilibrium of the linear cascade consisting of a single hairpin is 7 a.u. The maximum fluorescence at thermal equilibrium of the linear cascade consisting of 9 distinct hairpins is 57 a.u. To the first order approximation, the yield of 9 hairpins is approximated 79%. 0

11 5.5 ncentration (nm) Data - hairpin (x I) Data - hairpins (x I) Data - hairpins (x I) Data - 6 hairpins (x I) Data - 9 hairpins (x I) Model - hairpin (x I) Model - hairpins (x I) Model - hairpins (x I) Model - 6 hairpins (x I) Model - 9 hairpins (x I) Time (minutes) Figure S: Fitting the experimental results using the model proposed in the Supporting Information Section S: Scatter plots are experimental data; ine curves are fitted data using the least squares method[7]. The experimental results from Figure 6A were fitted using the least squares method[7]. Matlab scripts were detailed in Section SI S. Each experimental result was fitted to the corresponding cascade simulation. For example, the experimental result of nine hairpins was fitted using the cascade simulation of nine hairpins as shown in Script. As mentioned from prior discussion, the hairpins were designed to have the same structure with different nucleotide composition. The model assumed that the rate constant of each cascade reaction was equal. To determine this rate constant, Script was run until a final best- fit curve was obtained. This best- fit curve was resulted from minimizing the error function, which was the least squares error between the experimental data and the simulation data. Figure S shows the results from fitting the experimental data to the corresponding cascade simulations. The rate constants for systems of,,, 6, and 9 hairpins were fitted to be 0.97 x 0 6 /M/s, 0.85 x 0 6 /M/s, 0.58 x 0 6 /M/s,.0 x 0 6 /M/s, and. x 0 6 /M/s, respectively. These rate constants are independent of the cascade length and are approximately similar to the rate constant of the reporter complex (. x 0 6 /M/s). Note that the reporter complex was adopted from Zhang et al. [9]. Note that the fitted data reached the saturation level earlier than the experimental data. This discrepancy may be due to one or both of the following: i) improper synthesis or defects of DNA, or ii) the model does account for the fact that the actual system is not 00% efficient (i.e. all molecules from the model are assumed to participate in the reaction and this notion seems to be far- off from the actual observed experimental data).