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Molecular convolutional neural networks with DNA regulatory circuits

Nature Machine Intelligence volume 4, pages 625–635 (2022)Cite this article

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Abstract

Complex biomolecular circuits enabled cells with intelligent behaviour to survive before neural brains evolved. Since DNA computing was first demonstrated in the mid-1990s, synthetic DNA circuits in liquid phase have been developed as computational hardware to perform neural network-like computations that harness the collective properties of complex biochemical systems. However, scaling up such DNA-based neural networks to support more powerful computation remains challenging. Here we present a systematic molecular implementation of a convolutional neural network algorithm with synthetic DNA regulatory circuits based on a simple switching gate architecture. Our DNA-based weight-sharing convolutional neural network can simultaneously implement parallel multiply–accumulate operations for 144-bit inputs and recognize patterns in up to eight categories autonomously. Further, this system can be connected with other DNA circuits to construct hierarchical networks to recognize patterns in up to 32 categories with a two-step approach: coarse classification on language (Arabic numerals, Chinese oracles, English alphabets and Greek alphabets) followed by classification into specific handwritten symbols. We also reduced the computation time from hours to minutes by using a simple cyclic freeze–thaw approach. Our DNA-based regulatory circuits are a step towards the realization of a molecular computer with high computing power and the ability to classify complex and noisy information.

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Fig. 1: The ConvNet and its molecular implementation with DNA regulatory circuit systems.
Fig. 2: The DNA implementation of subfunctions and its experimental characterization.
Fig. 3: A convolution computation via multiple parallel MAC operations.
Fig. 4: A DNA-based ConvNet for the recognition of one of two rotated molecular patterns.
Fig. 5: The two-step classification approach based on a hierarchical network architecture for the recognition of 32 molecular patterns.
Fig. 6: A cyclic freeze–thaw approach to accelerate DNA circuits for molecular pattern recognition.

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Data availability

The data and experimental protocols associated with this work are included in the Supplementary Information available in the online version of the paper. Source data are provided with this paper.

Code availability

The code for the algorithm used for the network training in this work is available on Code Ocean and GitHub at https://doi.org/10.24433/CO.3022063.v150 and https://github.com/tongzhugroup/DNAcode.

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Acknowledgements

This work was supported by the National Science Foundation of China (grant nos. 21722502 and 22074041 to H.P.; 21991134 and T2188102 to C.F.) and the National Key Research and Development Program of China for International Science and Innovation Cooperation Major Project between Governments (2018YFE0113200 to H.P.).

Author information

Author notes

  1. These authors contributed equally: Xiewei Xiong, Tong Zhu.

Authors and Affiliations

  1. Shanghai Key Laboratory of Green Chemistry and Chemical Processes, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai, China

    Xiewei Xiong, Tong Zhu, Yun Zhu, Mengyao Cao, Jin Xiao, Li Li & Hao Pei

  2. School of Chemistry and Chemical Engineering, and Institute of Molecular Medicine, Renji Hospital, School of Medicine, Shanghai Jiao Tong University Shanghai, Shanghai, China

    Fei Wang & Chunhai Fan

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Contributions

H.P. initiated and supervised the research. X.X. conceived the research and designed and performed the experiments. H.P., T.Z. and X.X. discussed the design. Y.Z. and M.C. carried out experiments and interpreted data. J.X. and T.Z. developed the model and performed the in silico training. All authors analysed data. X.X., L.L., F.W., C.F. and H.P. wrote the manuscript.

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Correspondence to Hao Pei.

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Nature Machine Intelligence thanks Anne Condon, William Poole and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Five types of molecular structures used in the DNA circuits.

1, The weight substrate molecules NWt,Ii,j consist of three single strands. The loop portion is initially hybridized with a strand Bt to form rigid double helix structure, which forces the toehold and recognition domain apart, thus precluding the strand displacement. When the originally bound Bt falls off, the stems would be complementary to each other to form the hairpin loop structure, which bring the recognition domain and toehold domain in close proximity, thus favoring the branch migration through the recognition domain. 2, The summation gate Sdj,k is used to sum up all upstream weighted inputs from the same receptive region. The complexes Subn,Yi and double-stranded complexes Ddk,Yi were used for the subtraction (3 and 4). 3, Ddk,Yi can react with upstream strands to release the intermediate species Dsk,Yi. Note that Dsk,Yi would interact with the reporter RepYi with hairpin loop structure, and we added the spacer domain (‘TT’) to ensure the binding energy. 4, Subn,Yi consists of three single strands. In order to simplify the sequence design, we shortened the length of the inhibitory strand Inn that enable the rigid and double helix structure of Subn,Yi, to ensure that it can fully react with the upstream output strand. 5, RepYi could convert the upstream single strand to concentration-dependent fluorescent reporting signals by toehold-mediated strand displacement. The meaning of subscript indices of complexes, which are enclosed in coloured solid circles in the figure, is listed in the table. Different functional domains are represented by coloured lines.

Extended Data Fig. 2 The DNA implementation of a two-species MAC operation.

a, The abstract schematic of the MAC operation. The symbol ∑ indicates the sum over all inputs. b, The DNA implementation of two-input MAC operation. DNA species are represented by coloured solid and dotted circles, whereas different domains are represented by coloured lines. c, Fluorescence kinetics data of two-input MAC operation with different concentrations of weight tuning molecules MW1 and MW2. d, The steady fluorescence response of the output at 2.5 h with different concentrations of weight tuning molecules MW1 and MW2. Concentrations of weight substrate molecules NWt,Ii,j and inputs Xi are 2×, and concentration of the reporter RepY1 is 4×. The standard concentration is 50 nM (1× = 50 nM).

Extended Data Fig. 3 The DNA implementation of ConvNet.

a, The shared convolution kernel reacts with each receptive region to implement the weight multiplication. The value of each pixel in each receptive region was used to determine concentrations of each weight substrate molecules. For example, 23 nM for the 24th pixel and 32 nM for the 9th pixel. Different weight substrate molecules have distinct weight tuning domains (for example, NW24,I42,2 and NW9,I21,3). Because of the shared convolution kernel, the sequence of weight tuning domains (green region) of weight species is the same for each pixel that interacts with the same kernel function in different receptive regions (for example, NW24,I42,2 and NW24,I115,6). b, The recognition process of oracle ‘fire’ with the DNA-based ConvNet. c, The pooling layer reduces feature map size by taking the maximum value from a few contiguous pixels. The symbol ∑ indicates the sum over all inputs. Here, we used pooling computing to help identify which memory the pattern is the most similar—using the overall statistical characteristics of the adjacent output of a location to replace the output of the network at that location (pooling size 2×1, stride = 1). To realize the pooling computation, the two contiguous pixels—represented by concentrations of two distinct nucleic acids sequences—need to be compared to determine which is the largest. Note that the ‘annihilator’ gate in pooling layer was built based on the cooperative hybridization mechanism introduced by Cherry and Qian8. Coloured lines in DNA strands indicate distinct functional domains.

Extended Data Fig. 4 DNA logic circuits for classifying molecular patterns at coarse level.

a, Binary tags were attached to input patterns. Tags can take 1 and 0 as values, depending on whether a tag strand Tagj is present or absent, respectively. b, Abstract diagram of logic circuits that react with input Layer 1. For correctly computing the output for all classifiable patterns, the circuit requires 4 reporter gates and 4 fan-out gates. c, Abstract diagram for reporter gate R; red circle and black circle denote fluorophore and quencher, respectively. d, Abstract diagram for a fan-out gate F. Each fan-out gate is a node with two sides, one wire connected to the left side represents a DNA input strand (for example, input Tagj); 18 wires connected to the right side represents 18 gate strands that consist of a gate base strand (for example, Tagj-1) and an output strand (FMWt-j). Each output strand from fan-out gates contains a different weight tuning domain on the 5’ end to connect to downstream DNA neural networks. The gate base strand (Tagj-1) in each fan-out gate is the same to response to an input signal. e,f, Workflow of separation and purification of weight tuning molecules. e, Weight tuning molecules that were resulted from the fan-out gate, can be captured from total DNA strands using magnetic beads through hybridization reaction by biotinylated capture probes. By this way, non-target molecules can be removed, which may reduce the leakage and cross interactions from fan-out gates. Then, the beads were separated with a magnet for 3 mins, and washed 3 times to remove the supernatant, followed by resuspension in a buffer. The invader strand (Release) was then added to displace the weight tunning molecules from the beads. The supernatant was collected to switch on the DNA circuits to implement molecular pattern recognition. f, Immobilization of the capture probe (Capture) onto the streptavidin-functionalized magnetic beads. Coloured lines in DNA strands indicate distinct functional domains.

Extended Data Fig. 5 Cyclic freeze/thaw approach as drivers of DNA strand displacement.

a, The schematic diagram of freeze/thaw cycles process. Coloured lines in DNA strands indicate different functional domains, while coloured wavy lines represent DNA strands. b, The fluorescence levels of strand displacement after two freeze/thaw cycles (12 min) and 15 h at 25 °C. c, The fluorescence levels of strand displacement performed at 25 °C and with repeated freeze/thaw cycles, respectively. Red curve corresponds to kinetic trajectory for corresponding experiment carried out at 25 °C. Coloured dots correspond to the fluorescence levels of strand displacement after different cycles.

Supplementary information

Supplementary information

Supplementary discussion and Figs. 1–27.

Reporting summary

Supplementary Table 1

The DNA sequences.

Supplementary Table 2

Raw fluorescence data of supplementary figures.

Source data

Source Data Fig. 2

Fluorescence data.

Source Data Fig. 3

Fluorescence data.

Source Data Fig. 4

Fluorescence data.

Source Data Fig. 5.

Fluorescence data

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Xiong, X., Zhu, T., Zhu, Y. et al. Molecular convolutional neural networks with DNA regulatory circuits. Nat Mach Intell 4, 625–635 (2022). https://doi.org/10.1038/s42256-022-00502-7

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