SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION DOI:.38/NCHEM.246 Optimizing the specificity of nucleic acid hyridization David Yu Zhang, Sherry Xi Chen, and Peng Yin. Analytic framework and proe design 3.. Concentration-adjusted standard free energy G and hyridization yield (Text S) 3... Hyridization yield analysis of a standard X + C XC hyridization reaction (Fig. S) 4.2. Optimal discrimination factor Q max predicted y G (Text S2) 5.3. Relative thermodynamics of single-ase changes (Text S3) Tales of G values for single-ase changes (Tales S-S5) 8.4. Calculated hyridization yield for toehold exchange proes (Text S4).4.. Hyridization yield for a toehold exchange proe (Fig. S2) 2. Proe performance Band distriution after hour vs. after thermal annealing (Fig. S3) Verification of and intensity analysis (Fig. S4) Estimation of strand purity (Text S5) Predicted thermodynamics and hyridization yields of toehold exchange proes (Text S6) Sequences and energetics (Tale S6-S8) Additional experiments on X target Performance of the toehold exchange proes with varying concentrations of targets (Fig. S5) Effects of heterogeneous samples of correct and spurious targets on hyridization yield (Fig. S6) Fluorescence analysis of the X-7/5 proe (Fig. S7) 9 3. Target sequence generality Experimental results for X2-X5 systems (Fig. S8-) 2 4. Roustness Concentration dependence (Fig. S2) Temperature dependence (Fig. S3) Salt dependence (Fig. S4) Toehold exchange primers for PCR (Text S7) Heterogeneous mixture of 2 templates (Fig. S5) Templates with semi-repetitive sequence (Fig. S6-S7) Sequences (Tales S9-S) 29 NATURE CHEMISTRY

2 SUPPLEMENTARY INFORMATION2 Text S. Concentration-adjusted standard free energy G and hyridization yield 3 Text S2. Optimal discrimination factor Q max predicted y G 5 Text S3. Relative thermodynamics of single-ase changes 7 Text S4. Calculated hyridization yield for toehold exchange proes Text S5. Estimation of strand purity 3 Text S6. Predicted thermodynamics and hyridization yields of toehold exchange proes 3 Fig. S. Hyridization yield analysis of a standard X + C XC hyridization reaction 4 Fig. S2. Hyridization yield for a toehold exchange system Fig. S3. Band distriution after hour vs. after thermal annealing 2 Fig. S4. Method for quantitating hyridization yields from native PAGE results 2 Fig. S5. Performance of the toehold exchange proes with varying concentrations of targets 7 Fig. S6. Effects of heterogeneous samples of correct and spurious targets on hyridization yield 8 Fig. S7. Fluorescence studies of toehold exchange proes 9 Fig. S8. Experimental results for the X2 system 2 Fig. S9. Experimental results for the X3 system 2 Fig. S. Experimental results for the X4 system 2 Fig. S. Experimental results for the X5 system 22 Fig. S2. Concentration dependence of toehold exchange proes 23 Fig. S3. Temperature dependence of toehold exchange proes 23 Fig. S4. Salinity dependence of toehold exchange proes 24 Tale S. G of single-ase deletions 8 Tale S2. G of single-ase mismatches, A to N 8 Tale S3. G of single-ase mismatches, G to N 9 Tale S4. G of single-ase mismatches, C to N 9 Tale S5. G of single-ase mismatches, T to N Tale S6. Sequences and energetics of the protector (P ) and proe (PC) species 4 Tale S7. Sequences and energetics for the X, X2, and X3 systems. 5 Tale S8. Sequences and energetics for the X4 and X5 systems. 6 NATURE CHEMISTRY 2

3 SUPPLEMENTARY INFORMATION3 Text S. Concentration-adjusted standard free energy G and hyridization yield We first consider a standard X +C XC hyridization reaction. Let s assume the initial concentrations of X and C to e [X] = ac and [C] = c. For simplicity, let s define x [XC], the equilirium concentration of XC. χ = Without loss of generality, we assume that a, and the hyridization yield [XC] [XC] +[C] = x c. (If a<, then χ = [XC] [XC] +[X] value of x must satisfy the equilirium constant equation. = x ac, ut the mathematics work out similarly.) The K eq (ac x)(c x) = x K eq = [XC] [X] [C] x = (ac x)(c x) x = (a + )ck eq + 2K eq χ = x c = (a + )ck eq + 2cK eq (a ) 2 (ck eq ) 2 + 2(a + )ck eq + 2K eq (a ) 2 (ck eq ) 2 + 2(a + )ck eq + 2cK eq The value of the hyridization yield for various values of a are plotted in Fig. Sa, and for various operational concentrations c in Fig. S. As can e seen, the hyridization yield depends only on the concentration adjusted equilirium constant K eq = ck eq. χ = (a + )K eq + 2K eq (a ) 2 (K eq )2 + 2(a + )K eq + The hyridization yield is plotted against the concentration adjusted standard free energy G = RT ln(k eq) in Fig. Sc. 2K eq NATURE CHEMISTRY 3

4 SUPPLEMENTARY INFORMATION4 a Hyridization yield (χ) c = nm a = a = 2 a = 3 a = ΔG (kcal / mol) Hyridization yield (χ) nm μm, nm, nm μm nm ΔG (kcal / mol) ΔG (kcal / mol) c FIG. S: Hyridization yield analysis of a standard X + C XC hyridization reaction. (a) The hyridization yield is sigmoidal, and the exact shape depends on the stoichiometric ratio of X and C. () At different operational concentrations (shown are : stoichiometry plots), the hyridization yield varies. (c) The dimensionless concentration-adjusted standard free energy ( G ) effectively reflects the hyridization yields of the system. Extension to aritrary hyridization proes Similar analysis can e done for an aritrary hyridization proe reaction of the form: X + L i= Y i M i= Z i We will assume [X] = c, [Y i ] = a i c, and [Z i ] = i c for all i, with a i and i. At equilirium, [Z i ]= i c + x, and the hyridization yield is still defined as χ = x c. M i= K eq = [Z i] [X] L i= [Y i] M i= = ( ic + x) (c x) L i= (a ic x) M c L+ M i= K eq = ( i + χ) ( χ) L i= (a i χ) The change in the numer of species in the reaction is n = M (L + ), so the left-hand side can e rewritten as: K eq c n K eq = M i= ( i + χ) ( χ) L i= (a i χ) Solving this equation will yield an expression for χ that can e written solely in terms of K eq and constants L, M, a i and i. Consequently, the concentration adjusted equilirium constant K eq is an effective sole metric of hyridization yield. NATURE CHEMISTRY 4

5 SUPPLEMENTARY INFORMATION5 Text S2. Optimal discrimination factor Q max predicted y G Given that a correct target and a spurious target hyridize to a complement with standard free energy differing y G (see Fig. c, Tales S-S5), we can calculate the corresponding change in equilirium constant as z Q max e G /RT. Here, we show that this change in equilirium constant places an upper ound on the discrimination factor achievale. For convenience, we define K K eq to e the equilirium constant. x K = () (ac x)(c x) (ac x)(c x)k = x (2) (c x)kdx (ac x)kdx +(ac x)(c x)dk = dx (3) dk = (a + )ck 2xK + dx (4) (ac x)(c x) x = cχ dx = cdχ Recall that χ is a function of K; here χ(k) denotes the hyridization yield of a reaction with a particular K eq value. We want to show that: Q χ X χ S = χ(zk eq,s) χ(k eq,s ) < z χ(zk eq,s ) zk eq,s χ(k eq,s ) K eq,s < Because z>, it suffices to show that: d dk (χ(k) K ) < Kdχ χdk < K dx c x c dk < Kdx < xdk Sustituting equations () and (4) for K and dk, NATURE CHEMISTRY 5

6 SUPPLEMENTARY INFORMATION 6 x + )ck 2xK + dx < x(a dx (ac x)(c x) (ac x)(c x) < (a + )ck 2xK + 2x < (a + )c Recall that a, and c x; consequently, the aove inequality must e true. Thus, z Q max sets a limit on Q (with Q<zfor any K). Q max is a tight upper ound. Specifically, we prove that Q Q max as G + for the X +C XC and the X + PC XC + P reactions. First, for X + C XC: lim Q = K lim (χ X ) K χ S + )czk + (a ) = lim ((a 2 (czk) 2 + 2(a + )czk + K z((a + )ck + (a ) 2 (ck) 2 + 2(a + )ck + ) ) = (a + )czk + ( + (a + )czk 2ac2 z 2 K 2 ) z((a + )ck + ( + (a + )ck 2ac 2 K 2 )) = 2ac2 z 2 K 2 z(2ac 2 K 2 ) = z Consequently, z = e G /RT sets the upper ound for discrimination factor for a standard hyridization reaction, and this upper ound is approached as K eq approaches, and G approaches +. Next, for X + PC XC + P, with [X] = ac, [PC] = c, [XC] =, and [P ]=c, we get: (a + )K + ((a + )K + ) χ = 2 4a(K )K 2(K ) 2(K ) (a + )zk + lim Q = 2 + (2(a + ) +4a)zK +(a 2 +6a + )z 2 K 2 K (a + )zk (2(a + ) +4a)K +(a 2 +6a + )K 2 2azK (a + )zk + ( +(a + )zk + ) = (a + )K + ( +(a + )K + 2aK ) = 2azK 2aK = z with the exception of =, where (a + )zk 4azK +(a lim Q = 2 +6a + )z 2 K 2 K (a + )zk 4aK +(a 2 +6a + )K 2 (a + )zk 4azK (a + )K 4aK 4azK 4aK = z NATURE CHEMISTRY 6

7 SUPPLEMENTARY INFORMATION7 Discrimination factor at G = When G =, K eq,x =, and K eq,s = K eq,x z = z. We wish to determine a lower ound for discrimination factor Q = χ X χs, so we will compute a lower ound for χ X and an upper ound for χ S. Hyridization yield of X can e calculated as: χ X = a 2 +4 a 2. Calculation of dχ X da shows that χ X monotonically increases with a, so χ X =.38 is smallest value attainale (at a = ). K eq,s = cz = x (ac x)(c x) (ac x)(c x) x = cz < ac z χ S = x c < a z Consequently, Q = χ X χs > (.38)z; the discrimination factor at G = is within a constant factor of a the theoretical maximum of z. For a : stoichiometry, Q>.38z, within a factor of 3 of z. Discrimination factor at melting temperature At the melting temperature, χ X =.5. χ S < z Q = χ X χs =.5 χ S > z 2 Text S3. Relative thermodynamics of single-ase changes The standard free energy of a hyridization reaction is increased (made more positive) when a spurious target possesses even a single-ase change relative to the correct target. The relative thermodynamics of single-ase deletions are shown in Tale S, and that of single-ase changes are shown in Tales S2-S5, using values taken from SantaLucia and Hicks []. The relative thermodynamics of a single-ase insertion is +4. kcal/mol regardless of the identity of the inserted ase or the identities of the flanking ases. Listed G values are calculated as: G = G (SC) G (XC), where SC is the spuriously hyridized complex and XC is the correctly hyridized complex. All values are for M Na + at 37 C. As an example, the 5 -ACG-3 sequence normally pairs with 5 -CGT-3, yielding a standard free energy of G = G ( AC TG )+ G ( CG GC ) =.44 + ( 2.7) = 3.6 kcal/mol. A deletion of the middle C results in 5 -A-G-3, which yields standard free energy of G = G ( AG TC )+ G (ulge) = = kcal/mol, resulting in G =2.72 ( 3.6) = kcal/mol. A change of the middle C to a G results in 5 -AGG-3, which yields standard free energy of G = G ( AG TG )+ G ( GG GC )=.3+(.) =.24 kcal/mol, resulting in G =.24 ( 3.6) = kcal/mol. The G value sets the maximum discrimination factor, as descried previously. NATURE CHEMISTRY 7

8 SUPPLEMENTARY INFORMATION8 Deletion (average +5.4) A G C T A AAA +5. AAG +5. AAC +5. AAT +5. AGA AGG AGC +6.8 AGT ACA ACG ACC ACT ATA ATG +5.5 ATC ATT +5. G GAA +5. GAG GAC +4.5 GAT GGA GGG GGC GGT GCA GCG GCC GCT +6.8 GTA GTG +5.5 GTC +4.5 GTT +5. C CAA +5. CAG CAC +5.5 CAT +5.5 CGA +6.2 CGG CGC CGT CCA CCG CCC CCT CTA +4.4 CTG CTC CTT +5. T TAA +5. TAG +4.4 TAC TAT TGA +6.7 TGG TGC TGT TCA +6.7 TCG +6.2 TCC TCT TTA +5. TTG +5. TTC +5. TTT +5. TABLE S: Relative thermodynamics due to single-ase deletions range from +4.4 to kcal/mol, with mean of 5.4 kcal/mol. The middle ase shown in red is the original ase that is deleted. On average, an A or a T deletion results in kcal/mol, while a G or a C deletion results in kcal/mol. A to G (average +2.3) A G C T A AAA +3.5 AAG AAC AAT G GAA GAG GAC GAT C CAA CAG +.94 CAC +.83 CAT +.93 T TAA TAG +.97 TAC +.86 TAT +.96 A to C (average +3.66) A G C T A AAA AAG AAC +4.6 AAT G GAA GAG +3.6 GAC GAT C CAA CAG CAC CAT T TAA +3.3 TAG TAC TAT +3.6 A to T (average +3.8) A G C T A AAA AAG AAC AAT G GAA GAG +2.9 GAC GAT C CAA +3. CAG CAC CAT +2.9 T TAA TAG TAC +3.5 TAT TABLE S2: Relative thermodynamics due to single-ase changes from A to N range from +.83 to kcal/mol, with mean of +3. kcal/mol. The middle ase shown in red is the original ase that is changed. On average, changing an A to a G imposes a +2.3 kcal/mol penalty, changing an A to a C imposes a kcal/mol penalty, and changing an A to a T imposes a +3.8 kcal/mol penalty. NATURE CHEMISTRY 8

9 SUPPLEMENTARY INFORMATION9 G to A (average +4.98) A G C T A AGA AGG AGC AGT G GGA GGG GGC GGT C CGA +5.9 CGG CGC CGT +5.3 T TGA TGG +5. TGC +5.8 TGT G to C (average +5.33) A G C T A AGA AGG +5.5 AGC AGT G GGA GGG +5.7 GGC GGT +5.4 C CGA CGG +5.4 CGC +5.9 CGT T TGA TGG +5.4 TGC TGT G to T (average +4.9) A G C T A AGA AGG AGC AGT +4.9 G GGA GGG GGC GGT +4.9 C CGA +5.2 CGG +5.3 CGC CGT T TGA TGG TGC +5.6 TGT TABLE S3: Relative thermodynamics due to single-ase changes from G to N range from +4.9 to +5.9 kcal/mol, with mean of +5.8 kcal/mol. The middle ase shown in red is the original ase that is changed. On average, changing a G to an A imposes a kcal/mol penalty, changing a G to a C imposes a kcal/mol penalty, and changing a G to a T imposes a +4.9 kcal/mol penalty. C to A (average +3.56) A G C T A ACA ACG ACC +2.9 ACT G GCA +4.8 GCG GCC +3.3 GCT C CCA +4.6 CCG +4.5 CCC +3.9 CCT +3.7 T TCA +3.9 TCG +4. TCC +3.4 TCT +3.2 C to G (average +2.94) A G C T A ACA +3.2 ACG ACC +2.4 ACT G GCA +3.2 GCG +3.9 GCC +.86 GCT C CCA CCG CCC CCT T TCA TCG +3.8 TCC TCT C to T (average +3.45) A G C T A ACA ACG +3.2 ACC ACT +3.5 G GCA GCG GCC GCT C CCA +3.4 CCG CCC CCT +3.5 T TCA TCG TCC TCT TABLE S4: Relative thermodynamics due to single-ase changes from C to N range from +.86 to kcal/mol, with mean of kcal/mol. The middle ase shown in red is the original ase that is changed. On average, changing a C to an A imposes a kcal/mol penalty, changing a C to a G imposes a kcal/mol penalty, and changing a C to a T imposes a kcal/mol penalty. NATURE CHEMISTRY 9

10 SUPPLEMENTARY INFORMATION T to A (average +3.8) A G C T A ATA ATG ATC ATT +3. G GTA GTG GTC +3.8 GTT C CTA CTG CTC +3.8 CTT T TTA TTG TTC +3.6 TTT +3.3 T to G (average +2.4) A G C T A ATA +.9 ATG ATC +.95 ATT +2.4 G GTA +.92 GTG +2.4 GTC +.97 GTT +2.6 C CTA CTG CTC CTT T TTA TTG TTC TTT T to C (average +3.9) A G C T A ATA +3.5 ATG ATC ATT G GTA +3.4 GTG +4. GTC +4.2 GTT C CTA CTG CTC +4.8 CTT T TTA TTG TTC TTT +4.2 TABLE S5: Relative thermodynamics due to single-ase changes from T to N range from +.9 to kcal/mol, with mean of +3.7 kcal/mol. The middle ase shown in red is the original ase that is changed. On average, changing a T to an A imposes a +3.8 kcal/mol penalty, changing a T to a G imposes a +2.4 kcal/mol penalty, and changing a T to a C imposes a +3.9 kcal/mol penalty. NATURE CHEMISTRY

11 SUPPLEMENTARY INFORMATION Hyridization yield (χ) ΔG, = ΔG (kcal / mol) FIG. S2: Hyridization yield for a toehold exchange system with 2 X, P, and PC. For the main paper, [PC] = nm was typical. Text S4. Calculated hyridization yield for toehold exchange proes The reaction of a target X with the experimental toehold exchange proe PC can e written as follows: X + PC XC + P K eq = [XC][P ] [X][PC] For the reactions experimentally tested, we started with [PC] = c, [P ] = c, and [X] =2c. Define x =[XC] to e the concentration of hyridized product XC at equilirium. The hyridization yield is then χ = [XC] [XC] +[PC] = x c. K eq = [XC][P ] [X][PC] x(c + x) = (2c x)(c x) x = 3cK eq + c 2K eq 2 c χ = x c = 3K eq + 2K eq 2 K 2 eq + 4K eq + 2K eq 2 Keq 2 + 4K eq + 2K eq 2 Fig. S2 plots the analytic value of χ expected for a given reaction G = G. In the example reaction shown in Fig. 2a, G =.5 kcal/mol at 25 C, yielding K eq =.423 and χ =.343. NATURE CHEMISTRY

12 SUPPLEMENTARY INFORMATION 2 X ( hr) X (anneal) m6t ( hr) m6t (anneal) mt ( hr) mt (anneal) m6g ( hr) m6g (anneal) Control ( hr) Control (anneal) FIG. S3: Comparison of and distriution after hour of reaction and after thermal annealing for the X-7/6 toehold exchange system. Adjacent lanes show the species distriution after hour of reaction and after thermal annealing. In all cases, and distriutions were nearly identical for annealed versus isothermally reacted. This verifies that the reaction etween targets and the toehold exchange proe completes in hour. Fig. S7 further shows that even at nm concentration, equiliration is achieved in 2 minutes. a X mg m6t mt mc mg d ia it ic ig m6g Control 5% N = 56 7/ Frequency % 5% Total % Sum of and intensities in lane / average FIG. S4: Method for quantitating hyridization yields from native polyacrylamide gel electrophoresis (PAGE) results. (a) Quantitation of ands in the X 7/4 system (shown as the second gel in Fig. 3). The top and is PC and the ottom and is XC or SC, and their intensities are marked. Shown at the ottom is the sum of the intensities of the PC and XC ands. () Histogram of the sum of intensities of the PC and XC ands in each lane divided y the gel average. For example, the gel average for the gel shown in panel (a) is 9.8, so the data generated y the lanes in panel (a) would e =.9, 9.8 =.5, etc. This graphic comines data from the X, X2, X3, X4, and X5 systems (Fig. 3, Figs. S8-S). The standard deviation of this distriution is.66. Thus, the sum of the XC and PC and intensities are roughly preserved across lanes on the same gel, and hence the and intensities can e directly used to quantitate hyridization yield. NATURE CHEMISTRY 2

13 SUPPLEMENTARY INFORMATION 3 Text S5. Estimation of strand purity On the IDT wesite ( the company claims that that HPLC-purified strands will have purity of 85+%, while PAGE-purified strands will have purity of 9+%. This is consistent with the lead author s previous attempts to characterize the purity of oligonucleotides with post-synthesis purification [4], which showed that IDT strands with PAGE purification possessed 92-98% correct-length product. Taking the average of these values (95%), and assuming that the shorter-length oligonucleotides are (n-)-mers with a uniform distriution of deletions at every position, this results in roughly a.2% population of C with deletion at any particular position. For the.2% of C that possesses a deletion at position, the d spurious target would e perfectly matched and hyridize with high yield. This results in a minimum hyridization yield of.2, making the 7/6 system less sensitive than the 7/5 system. Text S6. Calculated hyridization yield for toehold exchange proes The standard free energies of strands and complexes are needed in order to calculate the standard free energy of reactions, which in turn can e used to generate the equilirium constant. For toehold exchange reactions, X + PC XC + P The standard free energy of the reaction is thus calculated as: G (reaction) = G (XC)+ G (P ) G (X) G (PC) The numerical G values (partition function) calculated for each strand and complex y NUPACK [2] are listed in Tales S6-S8. NATURE CHEMISTRY 3

14 SUPPLEMENTARY INFORMATION 4 Name Protector Sequence G (P ) G (PC) G (reaction with Correct) X-P7/6 T 3 TGCATCCACTCATTCAATACC X-P7/5 T 3 GCATCCACTCATTCAATACC X-P7/4 T 3 CATCCACTCATTCAATACC X-P7/ T 3 CACTCATTCAATACC X2-P7/5 T 3 ATGATTGAGGTAGTAGTTTG X2-P7/4 T 3 TGATTGAGGTAGTAGTTTG X3-P7/5 T 3 AGGATTTAATGCTAATCGTG X3-P7/4 T 3 GGATTTAATGCTAATCGTG X4-P7/5 T 3 CTCATCACTTGATACAAGCT X4-P7/4 T 3 TCATCACTTGATACAAGCT X5-P7/5 T 3 CGTTCCAAGAACAGATGTAC X5-P7/4 T 3 GTTCCAAGAACAGATGTAC TABLE S6: Sequences and energetics of the protector (P ) and proe (PC) species. Column shows the names of the various different protected complements PC, with the last numer representing the numer of ases that must spontaneously dissociate in order for the protector to e released. Column 2 shows the sequence of the protector P, with the T 3 denoting 3 continuous Thymines. The sequence of the complement strand can e derived from the sequence of the protector and that of the Correct target; for example, the sequence of the complement strand for X-P7/5 would e GACGTAGGGTATTGAAT- GAGTGGATGC. Columns 3 and 4 show the calculated standard free energies of the protector P and the protected complement PC, respectively (all energies given in kcal/mol). Column 5 shows the calculated standard free energy of the reaction X + PC XC + P, where X is the Correct target of the system (using the G values of X and XC given in Tales S7 and S8). NATURE CHEMISTRY 4

15 SUPPLEMENTARY INFORMATION 5 Name Sequence G (X or S) G (XC or SC) G X-Correct CACTCATTCAATACCCTACGTC X-mG GACTCATTCAATACCCTACGTC X-m6T CACTCTTTCAATACCCTACGTC X-mT CACTCATTCATTACCCTACGTC X-mC CACTCATTCACTACCCTACGTC X-mG CACTCATTCAGTACCCTACGTC X-d CACTCATTCA-TACCCTACGTC X-iA CACTCATTCAAATACCCTACGTC X-iT CACTCATTCATATACCCTACGTC X-iC CACTCATTCACATACCCTACGTC X-iG CACTCATTCAGATACCCTACGTC X-m6G CACTCATTCAATACCGTACGTC X2-Correct TGAGGTAGTAGTTTGTACAGTT X2-m2C TCAGGTAGTAGTTTGTACAGTT X2-m7T TGAGGTTGTAGTTTGTACAGTT X2-m2A TGAGGTAGTAGATTGTACAGTT X2-m7T TGAGGTAGTAGTTTGTTCAGTT X2-m7C TGAGGTAGTAGTTTGTCCAGTT X2-m7G TGAGGTAGTAGTTTGTGCAGTT X2-d7 TGAGGTAGTAGTTTGT-CAGTT X2-i7A TGAGGTAGTAGTTTGTAACAGTT X2-i7T TGAGGTAGTAGTTTGTTACAGTT X2-i7G TGAGGTAGTAGTTTGTGACAGTT X2-i7C TGAGGTAGTAGTTTGTCACAGTT X3-Correct TTAATGCTAATCGTGATAGGGT X3-m3T TTTATGCTAATCGTGATAGGGT X3-m8A TTAATGCAAATCGTGATAGGGT X3-m8G TTAATGCGAATCGTGATAGGGT X3-m8C TTAATGCCAATCGTGATAGGGT X3-d8 TTAATGC-AATCGTGATAGGGT X3-i8A TTAATGCATAATCGTGATAGGGT X3-i8T TTAATGCTTAATCGTGATAGGGT X3-i8G TTAATGCGTAATCGTGATAGGGT X3-i8C TTAATGCCTAATCGTGATAGGGT X3-m3C TTAATGCTAATCCTGATAGGGT X3-m8T TTAATGCTAATCGTGATTGGGT TABLE S7: Sequences and energetics of correct targets (X) and spurious targets (S) for the X, X2, and X3 systems. Column shows the names of the various different targets, and column 2 shows the sequence. Deviations from the correct target are shown in red, and - denotes a deletion. Columns 3 and 4 show the calculated standard free energies of the target T and the target-complement product complex TC (all energies given in kcal/mol). Column 5 shows the difference in standard free energies of the reaction with the correct target compared with the listed target. NATURE CHEMISTRY 5

16 SUPPLEMENTARY INFORMATION 6 Name Sequence G (X or S) G (XC or SC) G X4-Correct CACTTGATACAAGCTTACCATC X4-m4A CACATGATACAAGCTTACCATC X4-m9T CACTTGATTCAAGCTTACCATC X4-m4G CACTTGATACAAGGTTACCATC X4-m9G CACTTGATACAAGCTTACGATC X4-m9A CACTTGATACAAGCTTACAATC X4-m9T CACTTGATACAAGCTTACTATC X4-d9 CACTTGATACAAGCTTAC-ATC X4-i9C CACTTGATACAAGCTTACCCATC X4-i9G CACTTGATACAAGCTTACGCATC X4-i9A CACTTGATACAAGCTTACACATC X4-i9T CACTTGATACAAGCTTACTCATC X5-Correct CAAGAACAGATGTACCATCACA X5-m3T CATGAACAGATGTACCATCACA X5-m8T CAAGAACTGATGTACCATCACA X5-m3A CAAGAACAGATGAACCATCACA X5-m3C CAAGAACAGATGCACCATCACA X5-m3G CAAGAACAGATGGACCATCACA X5-d3 CAAGAACAGATG-ACCATCACA X5-i3A CAAGAACAGATGATACCATCACA X5-i3T CAAGAACAGATGTTACCATCACA X5-i3C CAAGAACAGATGCTACCATCACA X5-i3G CAAGAACAGATGGTACCATCACA X5-m8A CAAGAACAGATGTACCAACACA TABLE S8: Sequences and energetics of correct targets (X) and spurious targets (S) for the X4 and X5 systems. NATURE CHEMISTRY 6

17 SUPPLEMENTARY INFORMATION 7 a X m2c m7t m2a m7t m7c m7g d7 i7a i7t i7g i7c Control.5 [PC] = nm, [P] = nm 2 μm X 2 nm X 2 nm X Hyridization yield (χ) [X] (in nm) FIG. S5: Performance of the toehold exchange proes with varying concentrations of targets. (a) Native PAGE gel results. () Plot of hyridization yield as a function of target concentrations. The hyridization yield for 2 nm was calculated as χ = 5{XC} {XC}+{PC} (or its equivalent with SC), due to the fact that X or S were the limiting reagents. Due to the low intensities of the SC ands in the 2 nm gel, hyridization yields of spurious targets are less quantitatively reliale than that of other data points. NATURE CHEMISTRY 7

18 SUPPLEMENTARY INFORMATION 8 a T PC Xx + + CACTCATTCAATACCCTACGTC S CACTCATTCAATACCCTACGTC TTTT... P XxC T + P SC T + Xx Xx + mg Xx + m6t Xx + mt Xx + mc Xx + mg Xx + d Xx + ia Xx + it Xx + ic Xx + ig Xx + m6g Control Xx only c Control Xx Xx + Smix (. ) Xx + Smix (.25 ) Xx + Smix (.5 ) Xx + Smix ( ) Xx + Smix (2.5 ) Xx + Smix (5 ) Xx + Smix ( ) Xx + Smix (25 ) Xx + Smix (5 ) Xx + Smix ( ) Smix ( ) Tx only XxC Xx PC P SC XxC Xx PC P SC S S FIG. S6: Effects of heterogeneous samples of correct and spurious targets on hyridization yield. (a) Schematic of the experimental design. In order to distinguish XC from PC and SC, we appended a 6 nt poly-t tail to the 3 end of the correct target X; this modified target is referred to as Xx. Recall that the 5 end of protector P has a 3 nt poly-t tail. The proe used has toehold lengths of 7/5. () : mixtures of correct and spurious target. Each of lanes 2 through 2 show the reaction etween a mixture of the extended target Xx and one spurious target with the toehold exchange proe. Lane 3 ( Control ) shows the toehold exchange proe in the asence of any targets, and lane 4 ( Xx only ) shows the position of the extended target Xx for reference. The hyridization yield of the extended target Xx was oserved to e significantly higher than that of X (from Fig. 3), implying that the poly-t tail thermodynamically encourages the formation of a neary duplex either y stailizing the duplex or y destailizing the single-stranded Xx molecule. This is consistent with the oservation that P seems to ind more strongly to the complement C than predicted y NUPACK. (c) Effects of varying amounts of spurious target on the hyridization yield of the correct target. Smix denotes an equal mixture of all 2 spurious targets tested for this X system. [PC] = nm and [Xx] = 2 nm. As can e seen, even at 2 µm (total concentration of all S species), the mixture of spurious targets still did not ind significantly to the proe. Consequently, the hyridization yield of Xx was not significantly affected y the presence of varying amounts of the spurious target mixture. NATURE CHEMISTRY 8

19 SUPPLEMENTARY INFORMATION 9 a RQ ROX + + X PC XC P Fluorescence (nm) 5 [PC] = nm, [P] = nm 2 nm X 2 nm spurious mix 6 nm spurious mix 2 nm spurious mix 2 4 Time (min) c Fluorescence (nm).5 [PC] = nm, [P] = nm 2 nm X 2 nm spurious mix 6 nm spurious mix 2 nm spurious mix 2 4 Time (min) FIG. S7: Fluorescence studies of toehold exchange proes. (a) Schematic of the fluorophore/quencher-laeled proe. ROX denotes the caroxy-x-rhodamine fluorophore, and RQ denotes the Iowa Black Red Quencher (RQ). Upon reaction with a correct or spurious target, the quencher-functionalized protector strand is released, and the fluorescence of the solution is increased. () Time-ased fluorescence measurement of the operation of the toehold exchange proe at nm concentration. Species PC and P were in the cuvette initially, and correct target or the mixture of spurious targets was introduced at t. Listed concentration of the Spurious Mix denotes the total concentration of all spurious targets listed. At these concentrations, the toehold exchange reaction had completed in the 5 minutes it took to add target and mix the 4 samples. (c) Time-ased fluorescence measurement of the operation of the toehold exchange proe at nm concentration. The rate constant of the reaction is fitted to e 2 6 M s ; this value is within a factor of 2 of the rate constant of hyridizing two complementary strands of DNA [3]. These results suggest that the correct target will out-compete over x excess of spurious targets in hyridizing to the proe. NATURE CHEMISTRY 9

20 SUPPLEMENTARY INFORMATION 2 a X2 (let7g) X m2c m7t m2a m7t m7c m7g d7 i7a i7t i7g i7c Control TGAGGTAGTAGTTTGTACAGTT 7/4 ATGATTGAGGTAGTAGTTTG TACTAACTCCATCATCAAACATGTCAA 7/5 TGAGGTAGTAGTTTGTACAGTT TACTAACTCCATCATCAAACATGTCAA ATGATTGAGGTAGTAGTTTG c Hyridization yield (χ) Q =.6 to 7. Q = 3 to 58 7/4 Proe 7/5 d Hyridization yield (χ).75 Correct Spurious 7/4. kcal/mol / ΔG (kcal / mol) FIG. S8: Experimental results for the X2 system. (a) Schematic. Outlined in red are the positions of the one-ase changes in various spurious targets. () Native PAGE results. The protected complement was prepared at a 2: ratio of protector to complement, and annealed at µm concentration of PC. The correct or spurious targets were added to achieve final concentration 2 nm of target, nm of protected complement, and nm of free protector. All reactions proceeded at room temperature for hour. The gels show results when the pre-hyridized protector strand must spontaneously dissociate 5 or 4 ase pairs to e released; the 7 indicates that the intended target forms 7 new ase pairs upon hyridization. The left-most lane shows the reaction etween the correct target X and proe PC. Middle lanes each shows the reaction etween a spurious target S and PC; m denotes mismatch, d denotes deletion, and i denotes insertion (e.g. mc denotes that the A at position was replaced y a C). The right-most lane (laeled Control ) shows the PC and P solution without the introduction of any target. (c) Graphic summary of results from panel (). Shown in s are the hyridization yields of the correct target X; shown in dots are the hyridization yields of the spurious targets S. The hyridization yield of the correct target X is calculated as {XC} χ = {XC}+{PC}, where {XC} denotes the and intensity of XC. Hyridization yields were similarly calculated for spurious targets S. (d) Plot of oserved hyridization yield vs. yield predicted y reaction thermodynamics. The dark lack sigmoidal trace denotes the expected results, and the thin lack sigmoidal trace shows the expected results when all reaction standard free energies ( G ) are adjusted y +. kcal/mol. NATURE CHEMISTRY 2

21 SUPPLEMENTARY INFORMATION 2 a X3 (mir55) X m3t m8a m8g m8c d8 i8a i8t i8g i8c m3c m8t Control TTAATGCTAATCGTGATAGGGT 7/4 AGGATTTAATGCTAATCGTG TCCTAAATTACGATTAGCACTATCCCA 7/5 TTAATGCTAATCGTGATAGGGT TCCTAAATTACGATTAGCACTATCCCA AGGATTTAATGCTAATCGTG c Hyridization yield (χ) Q = 5 to 2+ Q = 2 to 2+ 7/4 7/5 Proe d Hyridization yield (χ) Correct Spurious 3.5 kcal/mol 7/4 7/ ΔG (kcal / mol) FIG. S9: Experimental results for the X3 system. (a) Schematic. () Native PAGE results. (c) Graphic summary of results from panel (). (d) Plot of oserved inding fraction vs. predicted reaction thermodynamics. The thin lack sigmoidal trace shows the expected results when all reaction standard free energies ( G ) are adjusted y +3.5 kcal/mol. a X4 (structured BM region) CA A TA CTTG CAAG CTTACCATC 7/4 X m4a m9t m4g m9g m9a m9t d9 i9c i9g i9a i9t Control CTCATCACTTGATACAAGCT GAGTAGTGAACTATGTTCGAATGGTAG 7/5 CACTTGATACAAGCTTACCATC GAGTAGTGAACTATGTTCGAATGGTAG CTCATCA A TA CTTG CAAG CTTACCATC c Hyridization yield (χ) Q = 2. to 4..5 Q = 3 to 2+ 7/4 7/5 Proe d Hyridization yield (χ) Correct Spurious.5 kcal/mol 7/4 7/ ΔG (kcal / mol) FIG. S: Experimental results for the X4 system. (a) Schematic. () Native PAGE results. (c) Graphic summary of results from panel (). (d) Plot of oserved inding fraction vs. predicted reaction thermodynamics. The thin lack sigmoidal trace shows the expected results when all reaction standard free energies ( G ) are adjusted y +.5 kcal/mol. NATURE CHEMISTRY 2

22 SUPPLEMENTARY INFORMATION 22 a X5 (structured toehold) CAAGAACA T AC GATG CATC ACA 7/4 X m3t m8t m3a m3c m3g d3 i3a i3t i3c i3g m8a Control CGTCCCAAGAACAGATGTAC GCAGGGTTCTTGTCTACATGGTAGTGT 7/5 fast fast c CAAGAACAGATGTACCATCACA GCAGGGTTCTTGTCTACATGGTAGTGT CGTCCCAAGAACAGATGTAC Hyridization yield (χ) Q =. to 2.3 Q = 3.5 to 34 7/4 Proe 7/5 d Hyridization yield (χ).75.5 Correct Spurious 7/ kcal/mol 7/ ΔG (kcal / mol) FIG. S: Experimental results for the X5 system. (a) Schematic. () Native PAGE results. (c) Graphic summary of results from panel (). (d) Plot of oserved inding fraction vs. predicted reaction thermodynamics. The thin lack sigmoidal trace shows the expected results when all reaction standard free energies ( G ) are adjusted y +.5 kcal/mol. NATURE CHEMISTRY 22

23 SUPPLEMENTARY INFORMATION 23 a X mg X CACTCATTCAATACCCTACGTC TGCATCCACTCATTCAATACC c Hyridization yield (χ) m6t mt mc mg d ia it ic ig m6g Control X mg nm μm ACGTAGGTGAGTAAGTTATGGGATGCAG 7/4 7/5 7/6 Proe nm μm.5 Q nm =.8 to 9.7 Q μm =.9 to 3 Q nm = 2 to 37 Q μm = 9. to 68 Q nm = 5. to 38 Q μm = 2.8 to 2 m6t mt mc mg d ia it ic ig m6g Control 7/4 7/5 7/6 FIG. S2: Concentration dependence of toehold exchange proes. (a) The X-7/4, X-7/5, and X-7/6 systems were tested at two different concentrations. Shown here is the schematic of the X-7/6 proe. () Experimental results. The left gel shows the results when initial concentrations were [X]=2 nm and [P ] =[PC] = nm (data repeated from Fig. 3), and the right gel shows the results when initial concentrations were [X] =2µM and [P ]= [PC] = µm. (c) Quantitation of results shown in panel (). a X-7/5 proe c CACTCATTCAATACCCTACGTC GCATCCACTCATTCAATACC CGTAGGTGAGTAAGTTATGGGATGCAG CACTCATTCAATACCCTACGTC CGTAGGTGAGTAAGTTATGGGATGCAG GCATCCACTCATTCAATACC o C 25 o C 37 o C X mg m6t mt mc mg d ia it ic ig m6g Control Hyridization yield (χ) Temperature ( o C) FIG. S3: Temperature dependence of toehold exchange proes. (a) The X-7/5 system that was tested at two additional temperatures, C and 37 C. () Experimental results. (c) Quantitation of results shown in panel (). NATURE CHEMISTRY 23

24 SUPPLEMENTARY INFORMATION 24 a X-7/5 proe CACTCATTCAATACCCTACGTC GCATCCACTCATTCAATACC CGTAGGTGAGTAAGTTATGGGATGCAG CACTCATTCAATACCCTACGTC CGTAGGTGAGTAAGTTATGGGATGCAG GCATCCACTCATTCAATACC.5 mm Mg 2+.5 mm Mg 2+ X mg m6t mt mc mg d ia it ic ig m6g Control 47.2 mm Mg [Mg 2+ ] (mm) c Hyridization yield (χ) FIG. S4: Salinity dependence of toehold exchange proes. (a) The X-7/5 system that was tested at two additional salt concentrations,.5 mm Mg 2+ and 47.2 mm Mg 2+. () Experimental results. (c) Quantitation of results shown in panel (). [] SantaLucia, J.; Hicks, D. Annu. Rev. Biophys. Biomol. Struct. 24, 33,, 45. [2] Dirks, R.M., Bois, J.S., Schaeffer, J. M., Winfree, E. & Pierce, N.A. Thermodynamic Analysis of Interacting Nucleic Acid Strands. SIAM Review 49, (27). [3] Zhang, D.Y. & Winfree, E. Control of DNA Strand Displacement Kinetics Using Toehold Exchange. J.Am.Chem.Soc. 3, (29). [4] Zhang, D.Y. & Winfree, E. Roustness and modularity properties of a non-covalent DNA catalytic reaction. Nucleic Acids Res. 38, (2). NATURE CHEMISTRY 24