Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Molecular convolutional neural networks with DNA regulatory circuits

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

Subjects

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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

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.

Similar content being viewed by others

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.

References

  1. Freedman, D. J. & Assad, J. A. Experience-dependent representation of visual categories in parietal cortex. Nature 443, 85–88 (2006).

    Article  Google Scholar 

  2. Zhong, L. et al. Causal contributions of parietal cortex to perceptual decision-making during stimulus categorization. Nat. Neurosci. 22, 963–973 (2019).

    Article  Google Scholar 

  3. Reinert, S., M Hübener, B. T. & Goltstein, P. M. Mouse prefrontal cortex represents learned rules for categorization. Nature 593, 411–417 (2021).

    Article  Google Scholar 

  4. Adleman, L. M. Molecular computation of solutions to combinatorial problems. Science 266, 1021–1024 (1994).

    Article  Google Scholar 

  5. Kim, J., Hopfeld, J. & Winfree, E. Neural network computation by in vitro transcriptional circuits. Adv. Neural Inf. Process. Syst. 17, 681–688 (2005).

    Google Scholar 

  6. Qian, L., Winfree, E. & Bruck, J. Neural network computation with DNA strand displacement cascades. Nature 475, 368–372 (2011).

    Article  Google Scholar 

  7. Genot, A. J., Fujii, T. & Rondelez, Y. Scaling down DNA circuits with competitive neural networks. J. R. Soc. Interface 10, 20130212 (2013).

    Article  Google Scholar 

  8. Cherry, K. M. & Qian, L. Scaling up molecular pattern recognition with DNA-based winner-take-all neural networks. Nature 559, 370–376 (2018).

    Article  Google Scholar 

  9. Linder, J. et al. Robust digital molecular design of binarized neural networks. In 2021 27th International Conference on DNA Computing and Molecular Programming (eds. Lakin, M. R. & Šulc, P.) https://drops.dagstuhl.de/opus/volltexte/2021/14668/ (Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2021).

  10. Kim, S. et al. Nanoparticle-based computing architecture for nanoparticle neural networks. Sci. Adv. 2, eabb3348 (2020).

    Article  Google Scholar 

  11. Soltoggio, A., Stanley, K. O. & Risi, S. Born to learn: the inspiration, progress, and future of evolved plastic artifcial neural networks. Neural Netw. 108, 48–67 (2018).

    Article  Google Scholar 

  12. Stanley, K. O., Clune, J., Lehman, J. & Miikkulainen, R. Designing neural networks through neuroevolution. Nat. Mach. Intell. 1, 24–35 (2019).

    Article  Google Scholar 

  13. Lecun, Y., Boser, B., Denker, J. S., Henderson, D. & Hubbard, W. Backpropagation applied to handwritten zip code. Neural Comput. 1, 541–551 (1989).

    Article  Google Scholar 

  14. Krizhevsky, A., Sutskever, I. & Hinton, G. ImageNet classification with deep convolutional neural networks. Proc. Adv. Neural Inf. Process. Syst. 25, 1090–1098 (2012).

    Google Scholar 

  15. LeCun, Y., Bengio, Y. & Hinton, G. Deep learning. Nature 521, 436–444 (2015).

    Article  Google Scholar 

  16. Al-Saffar, A., Hai, T. & Talab, M. A. Review of deep convolution neural network in image classification. In 2017 International Conference on Radar, Antenna, Microwave, Electronics, and Telecommunications (ICRAMET) pp 26–31 (IEEE, 2017).

  17. Luo, R., Sedlazeck, F. J., Lam, T. W. & Schatz, M. C. A multi-task convolutional deep neural network for variant calling in single molecule sequencing. Nat. Commun. 10, 998 (2019).

    Article  Google Scholar 

  18. Sahraeian, S. et al. Deep convolutional neural networks for accurate somatic mutation detection. Nat. Commun. 10, 1041 (2019).

    Article  Google Scholar 

  19. Hubel, D. H. & Wiesel, T. N. Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. J. Physiol. 160, 106–154 (1962).

    Article  Google Scholar 

  20. Yao, P. et al. Fully hardware-implemented memristor convolutional neural network. Nature 577, 641–646 (2020).

    Article  Google Scholar 

  21. Cong, I., Choi, S. & Lukin, M. D. Quantum convolutional neural networks. Nat. Phys. 15, 1273–1278 (2019).

    Article  Google Scholar 

  22. Xu, X. et al. 11 TOPS photonic convolutional accelerator for optical neural networks. Nature 589, 44–51 (2021).

    Article  Google Scholar 

  23. Wang et al. An in-memory computing architecture based on two-dimensional semiconductors for multiply–accumulate operations. Nat. Commun. 12, 3347 (2021).

    Article  Google Scholar 

  24. Feldmann, J. et al. Parallel convolutional processing using an integrated photonic tensor core. Nature 589, 52–58 (2021).

    Article  Google Scholar 

  25. Wu, C., Yu, H., Lee, S., Peng, R. & Li, M. Programmable phase-change metasurfaces on waveguides for multimode photonic convolutional neural network. Nat. Commun. 12, 96 (2021).

    Article  Google Scholar 

  26. Lai, W. et al. Programming chemical reaction networks using intramolecular conformational motions of DNA. ACS. Nano. 12, 7093–7099 (2018).

    Article  Google Scholar 

  27. Xiong, X. et al. Optochemical control of DNA switching circuits for logic and probabilistic computation. Angew. Chem. Int. Ed. 60, 3397–3401 (2021).

    Article  Google Scholar 

  28. Tang, Q. et al. Multi-mode reconfigurable DNA-based chemical reaction circuits for soft matter computing and control. Angew. Chem. Int. Ed. 60, 15013–15019 (2021).

    Article  Google Scholar 

  29. Pei, R., Matamoros, E., Liu, M., Stefanovic, D. & Stojanovic, M. N. Training a molecular automaton to play a game. Nat. Nanotechnol. 5, 773–777 (2010).

    Article  Google Scholar 

  30. Lakin, M. R., Minnich, A., Lane, T. & Stefanovic, D. Design of a biochemical circuit motif for learning linear functions. J. R. Soc. Interface 11, 20140902 (2014).

    Article  Google Scholar 

  31. Fernando, C. T. et al. Molecular circuits for associative learning in single-celled organisms. J. R. Soc. Interface 6, 463–469 (2009).

    Article  Google Scholar 

  32. Singh, A., Wiuf, C., Behera, A. & Gopalkrishnan, M. A reaction network scheme which implements inference and learning for Hidden Markov Models. In 2019 25th International Conference on DNA Computing and Molecular Programming (eds. Thachuk, C. & Liu, Y.) https://doi.org/10.48550/arXiv.1906.09410 (Springer, Cham, 2019).

  33. Wilhelm, D., Bruck, J. & Qian, L. Probabilistic switching circuits in DNA. Proc. Natl Acad. Sci. USA 115, 903–908 (2018).

    Article  Google Scholar 

  34. Seelig, G., Soloveichik, D., Zhang, D. & Winfree, E. Enzyme-free nucleic acid logic circuits. Science 314, 1585–1588 (2006).

    Article  Google Scholar 

  35. Morihiro, K., Ankenbruck, N., Lukasak, B. & Deiters, A. Small molecule release and activation through DNA computing. J. Am. Chem. Soc. 139, 13909–13915 (2017).

    Article  Google Scholar 

  36. Bertucci, A., Porchetta, A., Grosso, E. D., Patio, T. & Ricci, F. Protein-controlled actuation of dynamic nucleic acid networks using synthetic DNA translators. Angew. Chem. Int. Ed. 59, 20577–20581 (2020).

    Article  Google Scholar 

  37. Zhou, J. & Rossi, J. Aptamers as targeted therapeutics: current potential and challenges. Nat. Rev. Drug. Discov. 16, 181–202 (2017).

    Article  Google Scholar 

  38. Xiao, M., Lai, W., Wang, F., Li, L. & Pei, H. Programming drug delivery kinetics for active burst release with DNA toehold switches. J. Am. Chem. Soc. 141, 20354–20364 (2019).

    Article  Google Scholar 

  39. Xiao, M., Lai, W., Yu, H., Yu, Z. & Pei, H. Assembly pathway selection with DNA reaction circuits for programming multiple cell–cell interactions. J. Am. Chem. Soc. 143, 3448–3454 (2021).

    Article  Google Scholar 

  40. Lopez, R., Wang, R. & Seelig, G. A molecular multi-gene classifier for disease diagnostics. Nat. Chem. 10, 746–754 (2018).

    Article  Google Scholar 

  41. Zhang, C., Zhao, Y., Xu, X., Xu, R. & Han, D. Cancer diagnosis with dna molecular computation. Nat. Nanotechnol. 15, 709–715 (2020).

    Article  Google Scholar 

  42. Xiao, M., Lai, W., Man, T., Chang, B. & Pei, H. Rationally engineered nucleic acid architectures for biosensing applications. Chem. Rev. 119, 11631–11717 (2019).

    Article  Google Scholar 

  43. Douglas, S. M., Bachelet, I. & Church, G. M. A logic-gated nanorobot for targeted transport of molecular payloads. Science 335, 831–834 (2012).

    Article  Google Scholar 

  44. Benenson, Y., Gil, B., Ben-Dor, U., Adar, R. & Shapiro, E. An autonomous molecular computer for logical control of gene expression. Nature 429, 423–429 (2004).

    Article  Google Scholar 

  45. Thubagere, A. J., Thachuk, C., Berleant, J., Johnson, R. F. & Qian, L. Compiler-aided systematic construction of large-scale DNA strand displacement circuits using unpurified components. Nat. Commun. 8, 14373 (2017).

    Article  Google Scholar 

  46. Qian, L. & Winfree, E. Scaling up digital circuit computation with DNA strand displacement cascades. Science 332, 1196–1201 (2011).

    Article  Google Scholar 

  47. Zadeh, J. N. et al. NUPACK: analysis and design of nucleic acid systems. J. Theor. Comput. Chem. 32, 170–173 (2011).

    Article  Google Scholar 

  48. Bloice, M. D., Roth, P. M. & Holzinger, A. Biomedical image augmentation using augmentor. Bioinformatics 35, 4522–4524 (2019).

    Article  Google Scholar 

  49. Kingma, D. P. & Ba, J. A. A method for stochastic optimization. In Proc. International Conference on Learning Representations (ICLR, 2015).

  50. Xiong, X. et al. Molecular convolutional neural networks with DNA regulatory circuits. Code Ocean https://doi.org/10.24433/CO.3022063.v1 (2022).

  51. Zhang, D. Y. & Winfree, E. Control of DNA strand displacement kinetics using toehold exchange. J. Am. Chem. Soc. 131, 17303–17314 (2009).

    Article  Google Scholar 

  52. Zolaktaf, S. et al. Efficient parameter estimation for DNA kinetics modeled as continuous-time Markov chains. In 2019 25th International Conference on DNA Computing and Molecular Programming (eds. Thachuk, C. & Liu, Y.) https://resolver.caltech.edu/CaltechAUTHORS:20200811-134907797 (Springer, Cham, 2019).

Download references

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

Authors
  1. Xiewei Xiong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tong Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yun Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mengyao Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jin Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Li Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Fei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Chunhai Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Hao Pei
    View author publications

    You can also search for this author in PubMed Google Scholar

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.

Corresponding author

Correspondence to Hao Pei.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

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

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s42256-022-00502-7

This article is cited by

Search

Advanced search

Quick links

Nature Briefing AI and Robotics

Sign up for the Nature Briefing: AI and Robotics newsletter — what matters in AI and robotics research, free to your inbox weekly.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing: AI and Robotics