Typically, a domain level design specification can function with either orientation (5’-3’) for the DNA strands involved. However, it has been suggested in the literature [217] that certain 5’-3’
orientations for the molecules may be preferable in practice because of asymmetries in the distri- bution of synthesis errors along the 5’-3’ axis. In the hope that reversing 5’-3’ orientations might change the distribution of synthesis errors to a more favorable one, which may in turn result in
a
Rep Flux
BCjs*B hCj
hCj* F Q
React
CBCjsC
mC fB
s*C
sB
mB
f*B m*B s*B m*C
f*C
hCj
fB mB sB
hBr
Br
fC mC sC hCj
Cj
b
+
hCj QsB
mB
hCj
s*B hCj
hCj* F
+
Qs*B mB sB hCj
hCj* F
d c
Sample 2 Sample 1
Initial: 200 nM Rep FluxBCj (both samples)
+ 100 nM ReactCBCj 100 nM Br
+ 100 nM ReactCBCj
100 nM Br
Time t1
t2 ___ + 30 nM Cj
0 5 10 15
5 10 25 30
Initial leak
t1 t2
25 nM output FluxBCj output (nM)
Time (hours)
Figure 3.18: Reduced initial and gradual leaks in Design 3, illustrated withReactCBCj-Br leaks.
a. The molecules involved. RepFluxBCj is a reporter for FluxBCj, which works like Rep A in Figure3.15. For convenience the mechanism is illustrated in (b). c. Experimental setup. Both sample 1 and 2 contain 200 nM RepFluxBCjinitially, and 100 nMReactCBCjand 100 nM Br are added to both at timet1. The initial leak is under 5%, which is 2x-3x lower than in Designs 1 and 2. After the initial leak goes to completion, only Sample 2 is triggered with 30 nM of Cj at timet2. Note the fast triggering in Sample 2 and the much reduced gradual leak in Sample 1 (in general, 5x-10x lower than Design 1; see Figure3.15for an example). The apparent incompletion effect is also illustrated. Despite careful quantitation of all species, only 25 nM ofFluxBCj is released, which is about 16% less than the full 30 nM expected.
lower initial leak, we decided to try Design 3, which is the same as Design 2 but with 5’-3’ orien- tations reversed.
Since the free energy contributions of individual nearest-neighbor base pair stacks towards double helix stability are not symmetric with respect to 5’-3’ orientation, reversing the orientation of our design would perturb the thermodynamics of all our domains, including toeholds. This is an undesirable as it could potentially alter the kinetics of desired strand displacement pathways.
In spite of this, we went ahead with testing Design 3.
Experimentally, we found that Design 3 did have much lower initial leaks — reduced to 3-5%
of the fuel concentration (see Figure3.18). This was a big improvement from 10% in Designs 1 and 2. In addition, gradual leaks remained low, except in one particular case, that ofProduceCApAq andHelperAAq, where it was very high, approximately 150 /M /s.
Based on careful debugging experiments where we measured the gradual leak with various versions of theProduceCApAq andHelperAAq molecules, including 1-base mutations, we postu- lated a remote-toehold [216] style mechanism for the particularly high gradual leak rate (Fig- ure3.19). This particular gradual leak pathway is tackled in Design 4 (Section3.8).
While discussing these experimental results with Paul W. K. Rothemund, he suggested that performing these experiments with 0.5 - 1 MNa+(as opposed to 12.5 mMMg++, which was our protocol at that time) may result in lower gradual leak sinceMg++ is known to stabilize DNA- DNA junctions [194,236,237] and might be accelerating this gradual leak pathway by stabiliz- ing invasion of the Helper species at the junction. When we tested the gradual leak pathways in 0.5 MNa+, we found that there was a reduction in gradual leak across the board by approximately a factor of 2. So, we altered our protocol at this stage to use 0.5 MNa+instead of 12.5 mMMg++. Even though DNA strand displacement kinetics in high sodium (0.5 -1 MNa+) [145,146] is not dramatically different from kinetics in 12.5 mMMg++ [147], we experimentally verified that the kinetics of our desired pathways did not slowdown significantly due to the change in salt condi- tions (experiments not shown).
3.7.1 Kinetics of desired pathways
Apart from investigating leaks, we also experimentally checked whether the desired pathways (such as release of output in appropriate conditions) were occurring with (roughly) the expected kinetics. We found thatReactBABr andReactACAp were slow to “trigger” — that is, when both
inputs were present, these molecules were much slower to release their outputs than expected.
Compared toReactCBCj, where this triggering process takes about 20 minutes (Figure3.18), these molecules took about 10 hours (slower by a factor of 30).
We re-examined the MFE structures and partition functions of all the complexes involved in NUPACK. We found that hairpins had crept into both these strands, which were supposed to be free of secondary structure, during our last re-design (Figure3.20). In addition to the MFE structure, we found that the first two bases of the branch migration domainmA, both G’s, were bound almost all the time in some (weak) hairpin or the other. This location is especially critical, as initiation of the first branch migration step is known to be among the slowest unimolecular steps in the strand displacement process and is important in determining kinetics [148]. Given thatApandAqare common inputs to both React molecules, we hypothesized that this secondary structure was responsible for the slowdown in triggering both molecules.
Helper AAq
s*
Cf
Am
As
Af*
Ah
Aph
Ap*
h
Aqs
Am
Af
Af*
Ah
Aq*
Produce CApAq
hAq
fA fA
ATCC...
GGT A...
Figure 3.19: Based on experiments measuring gradual leak with single-base changes at the posi- tions illustrated (‘ATCC’ inHelperAAqand ‘GGTA’ inProduceCApAq), these bases contribute to the high gradual leak betweenProduceCApAqandHelperAAq. We hypothesize a remote-toehold type mechanism for this gradual leak; the complementarity between ‘CC’ ofHelperAAq and ‘GG’ of ProduceCApAqcould co-localize the molecules fleetingly to accelerate strand displacement, acting similarly to a strong 2-base pair toehold.
1.0
0.8
0.6
0.4
0.2
5 10 15 20 25 30 35 40 44 0.0
5 10 15 20 25 30 35
40 44
Free energy of strand (-kT log Q): -3.12 kcal/mol Pair probabilities at 25.0 C
Base index
Base index Equilibrium probability
1.0
0.8
0.6
0.4
0.2
5 10 15 20 25 30 35 40 44 0.0
5 10 15 20 25 30 35
40 44
Free energy of strand (-kT log Q): -2.47 kcal/mol Pair probabilities at 25.0 C
Base index
Base index Equilibrium probability
1.0
0.8
0.6
0.4
0.2
5 10 15 20 25 30 35 40 44 0.0
5 10 15 20 25 30 35
40 44
Free energy of strand (-kT log Q): -3.12 kcal/mol Pair probabilities at 25.0 C
Base index
Base index Equilibrium probability
1.0
0.8
0.6
0.4
0.2
5 10 15 20 25 30 35 40 44 0.0
5 10 15 20 25 30 35
40 44
Free energy of strand (-kT log Q): -2.47 kcal/mol Pair probabilities at 25.0 C
Base index
Base index Equilibrium probability
fA mA sA
hAp
a Ap
b
GG
fA mA sA hAq
GG
Aq
Figure 3.20: NUPACK predicted MFE structure and pair-probabilities matrix for Ap (a) and Aq (b). This secondary structure could slow down desired strand displacement pathways involving these molecules. In particular, the first two bases (GG) of the branch migration region are base paired most of the time and those base pairs occur as a part of several weak hairpins.