Thermodynamics and kinetics guided probe design for uniformly sensitive and specific DNA hybridization without optimization

Sensitive and specific DNA hybridization is essential for nucleic acid chemistry. Competitive composition of probe and blocker has been the most adopted probe design for its relatively high sensitivity and specificity. However, the sensitivity and specificity were inversely correlated over the length and concentration of the blocker strand, making the optimization process cumbersome. Herein, we construct a theoretical model for competitive DNA hybridization, which disclose that both the thermodynamics and kinetics contribute to the inverse correlation. Guided by this, we invent the 4-way Strand Exchange LEd Competitive DNA Testing (SELECT) system, which breaks up the inverse correlation. Using SELECT, we identified 16 hot-pot mutations in human genome under uniform conditions, without optimization at all. The specificities were all above 140. As a demonstration of the clinical practicability, we develop probe systems that detect mutations in human genomic DNA extracted from ovarian cancer patients with a detection limit of 0.1%.

Post-PCR genotyping and detection of low-abundance mutations. We first measured the concentrations of the human genomic DNA samples NA18537 (SMAD7-T homozygote) by Nanodrop 2000c spectrophotometer (Thermo Fisher). The sample was then diluted to a concentration of 50 ng µl -1 , and 1 µL of the diluted sample was added into a PCR tube to achieve a final concentration of 2.5 ng µl -1 (20 µL). After PCR, Exonuclease 1 (NEB) and Lambda exo (NEB) were added to degrade the double stranded PCR products and obtain single stranded DNA for further analysis. The detailed reactants for PCR were listed in Supplementary Table 4, and the thermal profiles were illustrated in Supplementary Table 5. The single stranded DNA were collected by a DNA purification kit (TIANquick Midi Purification Kit). After purification, the targeted single stranded DNA were treated with the probe/blocker composition system for fluorescence measurement. Thermodynamic model and analysis for standard probe/standard blocker system.

Supplementary
Since, We have, According to the mass-action equilibria for PMT formation, Combine the above four equations, Since, Similarly, The above equation is contradictory to the initial condition` of an increase in KBM. Conclusively, we have proved that the sensitivity is monotonically decreasing over [B] and KBM.
However, for specificity, we have to adopt the following approximations: Then, we could obtain much simpler analytic expressions of sensitivity and specificity over [B]0 and KBM, The relations between the involved free energy changes and equilibrium constants were as follows, The analytic expressions of sensitivity and specificity could be further transformed into, Then we adopted the following approximations: We could obtain the analytic expressions of sensitivity and specificity, The relations between the involved free energy changes were as follows, The analytic expressions of sensitivity and specificity could be further transformed into, Derivation of sensitivity, Thus, the sensitivity is monotonically decreasing over [B]0 and -∆GBW.
For the derivation of specificity, Then, Thus, the specificity is monotonically increasing over [B]0 and -∆GBW.
To sum up, Combine equations above, we could have, Then, we could obtain the quadric equation in [PMT], Similarly, we could obtain the quadric equation in [PWT].
The relations between the involved free energy changes were as follows, Combine the above two quadric equations, we could obtain analytic expressions of sensitivity over μBM, Define the sensitivity of a toehold probe alone toward targeting strand as F(x), in which the variable x was the equilibrium constant, Then, for PS + T→ PT + S, Combine the above four equations, we have Then, the expression of sensitivity could be simplified as, To figure out the monotonicity of sensitivity and specificity, we firstly needed to demonstrate the monotonicity of F(x), Where, Since, Thus, the sensitivity is monotonically decreasing over [B]0 and -∆GBW.
For specificity, we found that it was not always monotonically increasing over [B]0 and -∆GBW under all occasions. For certain thermodynamic parameters, the specificity curve could present small fluctuations when varying [B]0. But the amplitude of the fluctuations was so tiny that as a whole, the specificity seemed to be increasing over [B] 0 and -∆G BW . It was worth noting that for the modelling probe (probe-3) of Figure 2d, the specificity was rigorously increasing over [B]0 and -∆GBW. We then could calculate the limit of specificity, Therefore, the quasi value range of specificity was, Figure 2. The reaction pathways and levels of associated free energy changes in the Strand displacement probe/standard blocker system.
As was discussed in the main article, the above thermodynamic model required the Strand displacement probe/standard blocker system to reach thermodynamic equilibrium, which was impossible within several hours. Therefore, the actual reaction pathways were as follows, The thermodynamic equilibriums of first step and second step were independent and would not interfere with each other. Therefore, according to the mass-action equilibria, For the second step, we have, Combining the above equations, we could obtain, Introducing the relevant parameters of the modelling probe (Probe-3) into the above equations, we could draw the interception curves of the sensitivity and specificity over [B]0.
Modelling results showed that as [B]0 increased, the sensitivity decreased to around 0 whereas the specificity increased to the upper limit, in accordance with the experimental results.
Supplementary Figure 3. The predicted sensitivity and specificity of Strand displacement probe/standard blocker system. The equilibriums of reactions 1-2 and reactions 3-6 were assumed to be independent.

Thermodynamic model and analysis for dissociative 4-way strand-exchange led competitive
Combining equations above, we could have, Then, we could obtain the quadric equation in [PMT], Similarly, we could obtain the quadric equation in [PWT].
The relations between the involved free energy changes were as follows, Combine the above two quadric equations, we could obtain analytic expressions of sensitivity and specificity over μ, Then, the expression of sensitivity could be simplified as, Note that for the expression of sensitivity, no approximations were adopted. We could prove that the specificity  [BWT ] [BWT] 0 iii) Since F(KPM1) and F(KPM1)/F(KPBW) were completely accurate with no approximations at all, empirical rules could be applied to further eliminate the computer work. Many published papers have reported that for systems consisting of only probes and MT/WT, the near-optimal performance could be achieved simply by setting ∆GPM ≈ 0. In real applications, the 4-Way SELECT system was equivalent to a system consisting of only toehold probe and MT/WT. Therefore, such empirical rule of ∆GPM ≈ 0 could be applied to our system to make it completely optimization free, as was experimentally demonstrated in Figure 5. We also would like to point out that for dissociative 4-Way SELECT system, ∆GPM ≡ 0, so it was set to be optimization free by default.
For enhancing the performance of detection systems that already comprised probes: In many cases, researchers may have designed and synthesized strand displacement probes in their assays. But the experimental results, especially the specificity, were not satisfying. To improve the specificity, addition of a blocker strand into the system would be the first choice. In such situations, blockers, designed in the principle of the 4-Way SELECT system, showed huge advantages over other systems: when increasing the specificity of the system, conventional blocker would simultaneously lower down the system's sensitivity, whereas our proposed blocker would not affect the sensitivity at all. Especially for enhancing the specificity of multiplexed assays targeting multiple mutations of interests, our system was extremely convenient to employ and would be the best choice.