Accelerating DNA computing via freeze-thaw cycling

DNA computing harnesses the immense potential of DNA molecules to enable sophisticated and transformative computational processes but is hindered by low computing speed. Here, we propose freeze-thaw cycling as a simple yet powerful method for high-speed DNA computing without complex procedures. Through iterative cycles, we achieve a substantial 20-fold speed enhancement in basic strand displacement reactions. This acceleration arises from the utilization of eutectic ice phase as a medium, temporarily increasing the effective local concentration of molecules during each cycle. In addition, the acceleration effect follows the Hofmeister series, where kosmotropic anions such as sulfate (SO42−) reduce eutectic phase volume, leading to a more notable enhancement in strand displacement reaction rates. Leveraging this phenomenon, freeze-thaw cycling demonstrates its generalizability for high-speed DNA computing across various circuit sizes, achieving up to a remarkable 120-fold enhancement in reaction rates. We envision its potential to revolutionize molecular computing and expand computational applications in diverse fields.


Figures and Tables
Fig. S1.Schematic of the experimental system used for reporting when operated in freeze-thaw cycling or operated at 25 ℃.The DNA implementation of reporting either with (A) freeze-thaw cycling or with (B) operation at 25 ℃.In freezethaw cycling, reporter R8 (toehold = 8 nt) reacted with an output strand (Out) released from Cm,8, converting the output signal (Out) to a fluorescence signal.When operation at 25 ℃, reporter Cm,8,R was used to directly reacted with an input strand (Xm,8), yielding a fluorescence signal.The red dot represents the fluorescent group of FAM, and the black dot represents the quencher group of BHQ-1.(C) Left: The fluorescence reporting kinetics (left) of different concentrations of strand Out reacting with R8 in room temperature; Right: Linear relationships were obtained between the concentrations of strand Out and the steadystate fluorescence response.The data showed that reporting could be implemented rapidly within 5 min and reporter R8 could react stoichiometrically with product generated after freeze-thaw cycling.Reporter R8 was added in solution with relative concentrations of 1×.(D) Gray curve: R8 were mixed in solution with relative concentrations of 1×, input strand (X5,8) and complex strand (C5,8) were then added with relative concentrations of 1×; Blue curve: Reporter (C5,8,R) was added in solution with relative concentrations of 1×, input strand (X5,8) was then added at 1×.We observed that two reactions achieved the same equilibrium yields, which indicates that the separate reporter R8 could accurately report the output signal generated in freezethaw cycling process.The standard concentration is 50 nM (1× = 50 nM).Weight complex (Wi), switching complex (Swi), transmit complex (Sdi), complex (Cm,8) and reporter (Cm,8,R or R8) were at 1×, 2×, 4×, 1×, and 1×, respectively (standard concentration 1× = 50 nM).Reporter Cm,8,R was used for signal readout at 25 ℃, and reporter R8 was used for signal readout during freeze-thaw cycling.Input strands were at 0× or 2×. Circuit computes either OR or AND through the adjustment of initial concentration of the threshold (Thi).Freeze-thaw cycling Table S3.
All DNA sequences used in this work.

Fig. S3 .
Fig. S3.Freeze-thaw cycling accelerates DNA strand displacement reaction in the presence of different counterions.(A to C) Repeated freeze-thaw cycling sped up the DNA strand displacement reaction in the presence of different counterions (A: Ac − , B: Cl − , C: NO3 − ).(D) The average rates of the DNA hybridization of complementary DNA strands was calculated as the ratio of the corresponding output level versus the required cycles of freeze-thaw in the absence of input strand (X4,8).Data are represented as mean ± s.d. of n = 3 independent experiments.

Fig. S5 .
Fig. S5.Freeze-thaw cycling accelerates OR logic gate.(A) The fluorescence kinetics data of OR logic gate when operated at 25 ℃.(B) Comparisons of the fluorescence level of outputs after 1 freeze-thaw cycle (left) and at 1.5 h operated at 25 ℃ (right).(C) The fluorescence level of outputs through repeated freeze-thaw cycles.(D) Comparisons of the fluorescence level of outputs after 5 freeze-thaw cycles (left) and at 4 h operated at 25 ℃ (right).Data are represented as mean ± s.d. of n = 3 independent experiments.The initial concentration of threshold (Thi) was 0×.Experiments were conducted in TE buffer (pH 8.0) containing 12.5 mM MgSO4.The gray dotted line marks the threshold value of 0.4.The standard concentration is 50 nM (1× = 50 nM).

Fig. S6 .
Fig. S6.Freeze-thaw cycling accelerates AND logic gate.(A) The fluorescence kinetics data of AND logic gate when operated at 25 ℃.(B) Comparisons of the fluorescence level of outputs after 2 freeze-thaw cycle (left) and at 6 h operated at 25 ℃ (right).(C) The fluorescence level of outputs through repeated freeze-thaw cycles.(D) Comparisons of the fluorescence level of outputs after 5 freeze-thaw cycles (left) and at 16 h operated at 25 ℃ (right).Data are represented as mean ± s.d. of n = 3 independent experiments.The initial concentration of threshold (Thi) is 0.8× (Standard concentration 1× = 50 nM).Experiments were conducted in TE buffer (pH 8.0) containing 12.5 mM MgSO4.The gray dotted line marks the threshold value of 0.4.

Fig. S7 .
Fig. S7.Ion identity affects the acceleration effect of OR logic gate.(A) Left: Freeze-thaw cycling speeds up OR logic in the presence of different counterions; Right: Truth table.(B) Fluorescence levels of the OR logic gate through repeated freezethaw cycles when using Ac − (green), Cl − (red), and NO3 − (gray) as magnesium counterion, respectively.(C) The fluorescence levels of the circuit that reached completion either with freeze-thaw cycling (blue zone) or with operation at 25 °C (blank zone) when using different magnesium counterions (Ac − , Cl − , NO3 − ).Data are represented as mean ± s.d. of n = 3 independent experiments.The numbers in the rings represented the time required for the repeated freeze-thaw cycling or operation at 25 ℃.Experiments were conducted in a TE buffer (pH 8.0) containing 12.5 mM (CH3COO)2Mg, MgCl2, or Mg(NO3)2, respectively.The gray dotted line marks the threshold value of 0.4 (solid dots for ON, empty dots for OFF).

Fig. S8 .
Fig. S8.Ion identity affects the acceleration effect of AND logic gate.(A) Left: Freeze-thaw cycling speeds up AND logic in the presence of different counterions; Right: Truth table.(B) Fluorescence levels of the AND logic gate through repeated freeze-thaw cycles in the presence of Ac − ( green), Cl − (red), and NO3 − (gray), respectively.(C) The fluorescence levels of the circuit that reached completion either with freeze-thaw cycling (blue zone) or with operation at 25 °C (blank zone) when using different magnesium counterions (Ac − , Cl − , NO3 − ).Data are represented as mean ± s.d. of n = 3 independent experiments.The number in the rings represented the time required for repeated freeze-thaw cycling or operation at 25 ℃.Experiments were conducted in a TE buffer (pH 8.0) containing 12.5 mM (CH3COO)2Mg, MgCl2, or Mg(NO3)2, respectively.The gray dotted line marks the threshold value of 0.4 (solid dots for ON, empty dots for OFF).

Fig. S9 .
Fig. S9.Two-layer circuit.(A) Kinetics experiments.(B) Distinct species and corresponding concentrations used in the circuit.Repeated freeze-thaw cycles were used to accelerate two-layer DNA circuit in the presence of (C) SO4 2-or other counterions (D) Ac − , Cl − , NO3 − .(E) The fluorescence levels of the circuit that reached completion either with freeze-thaw cycling (blue zone) or with operation at 25 °C (blank zone) when using different magnesium counterions (Ac − , Cl − , NO3 − ).Data are represented as mean ± s.d. of n = 3 independent experiments.Experiments were conducted in a TE buffer (pH 8.0) containing 12.5 mM MgSO4, (CH3COO)2Mg, MgCl2, or Mg(NO3)2, respectively.The numbers in the rings represented the time required for repeated freeze-thaw cycling or operation at 25 ℃.The gray dotted line marks the threshold value of 0.4 (solid dots for ON, empty dots for OFF).

Fig. S10 .
Fig. S10.Three-layer circuit.(A) Kinetics experiments.(B) Distinct species and corresponding concentrations used in the circuit.Repeated freeze-thaw cycles were used to accelerate three-layer DNA circuit in the presence of (C) SO4 2-or other counterions (D) Ac − , Cl − , NO3 − .(E) The fluorescence levels of the circuit that reached completion either with freeze-thaw cycling (blue zone) or with operation at 25 °C (blank zone) when using different magnesium counterions (Ac − , Cl − , NO3 − ).Data are represented as mean ± s.d. of n = 3 independent experiments.Experiments were conducted in a TE buffer (pH 8.0) containing 12.5 mM MgSO4, (CH3COO)2Mg, MgCl2, or Mg(NO3)2, respectively.The numbers in the rings represented the time required for repeated freeze-thaw cycling or operation at 25 ℃.The gray dotted line marks the threshold value of 0.4 (solid dots for ON, empty dots for OFF).

Fig. S11 .
Fig. S11.The DNA implementation of DNA-based convolutional neural network (ConvNet).(A) The original handwritten symbols were converted to binary patterns where each 1 or 0 corresponds to the presence and absence of the input strand.The concentration of each input strand is 200 nM.(B) The DNA implementation of the convolution kernel with dimensions of 3×6.Each weight value of each pixel in the convolution kernel determines the concentration of the weight substrate molecule NWt,Ii,j (for example, 21 nM for the 5th pixel).Each weight can be encoded in a distinct sequence of weight tuning domain (for example, blue domains W5* and green domains W16*).Note that positive and negative weights are implemented by using different output sequences of NWt,Ii,j (for example, Pj in NW5,Ii,j and Pi in NW16,Im,i).(C) Each receptive region (red dashed box) of a '3' reacts with the same convolution kernel to export feature maps, where weight tuning molecule MWt activates the corresponding weight substrate molecule NWt,Ii,j in eight receptive regions in parallel.(D) The number of distinct molecular species used in the DNA-based ConvNet.

Fig. S14 .
Fig. S14.Repeated freeze-thaw cycling speeds up large-scale DNA-based ConvNet when using Cl − as magnesium counterion.Through repeated freeze-thaw cycling, we found that computation of this network circuit was accelerated, in which 5 cycles of freeze-thaw allowed each input patterns to trigger the almost same output level as operating at 25 ℃.The numbers in the rings represented the time required to complete the pattern recognition with the repeated freeze-thaw cycling or operation at 25 ℃.Note that when negative counterions were changed, we could barely observe detectable changes in behavior of circuit operated at 25 ℃.Experiments were conducted in TE (pH 8.0) buffer containing 12.5 mM MgCl2 (freezethaw cycling) or MgSO4 (operation at 25 ℃).

Fig. S15 .
Fig. S15.Repeated freeze-thaw cycling speeds up large-scale DNA-based ConvNet when using NO3 − as magnesium counterion.Through repeated freeze-thaw cycling, we found that computation of this network circuit was accelerated, in which 7 cycles of freeze-thaw allowed each input patterns to trigger the almost same output level as operating at 25 ℃.The numbers in the rings represented the time required to complete the pattern recognition with the repeated freeze-thaw cycling or operation at 25 ℃.Note that when negative counterions were changed, we could barely observe detectable changes in behavior of circuit operated at 25 ℃.Experiments were conducted in TE (pH 8.0) buffer containing 12.5 mM MgCl2 (freezethaw cycling) or MgSO4 (operation at 25 ℃).