Gated Transient Dissipative Dimerization of DNA Tetrahedra Nanostructures for Programmed DNAzymes Catalysis

Transient dissipative dimerization and transient gated dimerization of DNA tetrahedra nanostructures are introduced as functional modules to emulate transient and gated protein–protein interactions and emergent protein–protein guided transient catalytic functions, operating in nature. Four tetrahedra are engineered to yield functional modules that, in the presence of pre-engineered auxiliary nucleic acids and the nicking enzyme Nt.BbvCI, lead to the fueled transient dimerization of two pairs of tetrahedra. The dynamic transient formation and depletion of DNA tetrahedra are followed by transient FRET signals generated by fluorophore-labeled tetrahedra. The integration of two inhibitors within the mixture of the four tetrahedra and two auxiliary modules, fueling the transient dimerization, results in selective inhibitor-guided gated transient dimerization of two different DNA tetrahedra dimers. Kinetic models for the dynamic transient dimerization and gated transient dimerization of the DNA tetrahedra are formulated and computationally simulated. The derived rate-constants allow the prediction and subsequent experimental validation of the performance of the systems under different auxiliary conditions. In addition, by appropriate modification of the four tetrahedra structures, the triggered gated emergence of selective transient catalytic functions driven by the two pairs of DNA tetrahedra dimers is demonstrated.

The principles to design such transient system should include the following rules: -The stability of the different duplexes involved in the reaction module are determined by the number and nature of base pairs. The energetic stabilization of the duplex is estimated using NUPACK software.
-The energetic stabilization of the rest reaction module is controlled by the energy level of the duplex L1/I1.
-The triggered transition of the rest module to the transient T1/T2 tetrahedra structure requires the intermediate products L1/L1' and I1/T1T2 dimer that should be energetically more stable than L1/I1.
-The cleavage of the duplex L1/L1' separates the "waste" products of the fragmented pieces of L1'. The released L1 displaces I1 from the dimer I1/T1T2 guided by the enhanced energetic stability of L1/I1 as compared to I1/T1T2.
The following scheme outlines the relative energy levels of the constituents associated with the transient operation of the network.  It should be noted that the format of plotting the calibration curve yields a non-linear increase. This can be quantitatively rationalized as follows: For this low concentration (1 μM) system, the fluorescence intensities of Cy3 (F1) and Cy5 (F2) are given by equation (i) and equation (ii): where Cy5/Cy3 corresponds to the concentration of Cy5 in the FRET luminescent complex composed of I1/T1T2.
Since the start concentration of Cy3 is 1μM, the transient concentration of Cy3 is given by equation Thus, the ratio of F2/F1 is given by equation (iv) that can be rewritten as follows: (iv) That is, the ratio of F2/F1 follows a classical parabolic function f = k * It is important to note that the computationally simulated rate constants have a meaning only if one or more of the rate-constants can be evaluated independently experiment and computationally, and the result should be compared to the analogy rate-constant being part of the overall kinetic model. According the values of k3 and k-3 in the presence of two concentrations of I1 were evaluated as follows, Figure S5.

Experimental (i)-dotted lines and computationally (ii)-dashed lines
Evaluation of the rate constants k3 and k−3 of the kinetic scheme in Figure S4.
To evaluate the rate constants k3 and k−3 appearing in the kinetic scheme, equation (3) in Figure S4, the mixture of T1 and T2 (1 μM each) was subjected to two different concentrations of I1 (0.4 μM and 0.8 μM), and the time-dependent concentration changes were evaluated by following the time-dependent fluorescence changes of the tetrahedron dimers associated with T1/T2, and translating them into concentrations by applying an appropriate calibration curve, Figure S3. From the kinetic profiles and using the Matlab R2020a program, the respective k3 = 5 μM -2 min -1 and k−3 = 0.0236 min -1 were derived. These values fit well with the computationally simulated rate constant following the overall kinetic model and Table S1.  It is important to note that the computationally simulated rate constants have a meaning only if one or more of the rate-constants can be evaluated independently experiment and computationally, and the result should be compared to the analogy rate-constant being part of the overall kinetic model. According the values of k9 and k-9 in the presence of two concentrations of I2 were evaluated as follows, Figure S10.

Experimental (i)-dotted lines and computationally (ii)-dashed lines
Evaluation of the rate constants k9 and k−9 of the kinetic scheme in Figure S9.
To evaluate the rate constants k9 and k−9 appearing in the kinetic scheme, equation (9) in Figure S9, the mixture of T3 and T4 (1 μM each) was subjected to two different concentrations of I2 (0.3 μM and 1.2 μM), and the time-dependent concentration changes were evaluated by following the time-dependent fluorescence changes of the tetrahedron dimers associated with T3/T4, and translating them into contents by applying an appropriate calibration curve, Figure S7. From the kinetic profiles and