Skip to main content
SpringerLink
Log in

Molecular device design based on chemical reaction networks: state feedback controller, static pre-filter, addition gate control system and full-dimensional state observer

  • Original Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

For the modeling and operation of biological computing, chemical reaction networks (CRNs) constitute an ideal programming paradigm for the simulation of various digital and analog circuits. In this manuscript, an originally divergent linear time-invariant (LTI) CRNs system is made stable by constructing a state feedback controller. State feedback controllers control the internal characteristics of a linear system through the state matrix of the system. A static pre-filter based on CRNs is constructed in order to ensure the tracking effect of system response. Next, considering extraneous disturbances to the LTI system, an integration element is added in the first channel of the control system to stably suppress disturbance input. Moreover, the state feedback controller is utilized to build an addition gate control system. When a leak reaction occurs in the addition gate, the addition gate control system produces the correct calculation result, whereas the addition gate calculation is wrong. Finally, a full-dimensional state observer based on CRNs is implemented in this paper. In the case of external disturbance interference or incomplete modeling, the state trajectories of the system are observed by the full-dimensional state observer.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Code availability

Visual DSD.

References

  1. S. Ranallo, C. Prévost-Tremblay, A. Idili, Antibody-powered nucleic acid release using a DNA-based nanomachine. Nat. Commun. 8, 15150 (2017)

    Article  CAS  Google Scholar 

  2. J. Duan, W. Li, X. Li, Molecular design of DNA polyhedra based on genus. J. Math. Chem. 52, 2380–2394 (2014)

    Article  CAS  Google Scholar 

  3. P. Zhang, J. Jiang, R. Yuan, Highly ordered and field-free 3D DNA nanostructure: the next generation of DNA nanomachine for rapid single-step sensing. J. Am. Chem. Soc. 140, 9361–9364 (2018)

    Article  CAS  Google Scholar 

  4. X. Zhang, Q. Zhang, Y. Liu, A molecular device: a DNA molecular lock driven by the nicking enzymes. Comput. Struct. Biotechnol. J. 18, 2107–2116 (2020)

    Article  CAS  Google Scholar 

  5. K. Chen, J. Kong, J. Zhu, Digital data storage using DNA nanostructures and solid-state nanopores. Nano Lett. 19, 1210–1214 (2018)

    Article  Google Scholar 

  6. B. Cao, B. Wang, Q. Zhang, Designing uncorrelated address constrain for DNA storage by DMVO algorithm. IEEE/ACM Trans. Comput. Biol. Bioinform. (2020). https://doi.org/10.1109/TCBB.2020.3011582

    Article  PubMed  Google Scholar 

  7. H. Fu, H. Lv, Q. Zhang, Using entropy-driven amplifier circuit response to build nonlinear model under the influence of Lévy jump. BMC Bioinform. 22, 437 (2022)

    Article  CAS  Google Scholar 

  8. P. Wąż, D. Bielińska-Wąż, A. Nandy, Descriptors of 2D-dynamic graphs as a classification tool of DNA sequences. J. Math. Chem. 52, 132–140 (2014)

    Article  Google Scholar 

  9. H. Lv, H. Li, Q. Zhang, Analysis of periodic solution of DNA catalytic reaction model with random disturbance. IEEE Open J. Nanotechnol. 2, 140–147 (2021)

    Article  Google Scholar 

  10. R. Daniel, J. Rubens, R. Sarpeshkar, Synthetic analog computation in living cells. Nature 497, 619–623 (2013)

    Article  CAS  Google Scholar 

  11. D. Wilhelm, J. Bruck, L. Qian, Probabilistic switching circuits in DNA. Proc. Natl Acad. Sci. U.S.A. 115, 903–908 (2018)

    Article  CAS  Google Scholar 

  12. C. Liu, Y. Liu, Q. Zhang, Cross-inhibitor: a time-sensitive molecular circuit based on DNA strand displacement. Nucleic Acids Res. 48, 10691–10701 (2020)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  15. D. Soloveichik, G. Seelig, E. Winfree, DNA as a universal substrate for chemical kinetics. Proc. Natl Acad. Sci. U.S.A. 107, 5393–5398 (2010)

    Article  CAS  Google Scholar 

  16. Y. Chen, N. Dalchau, N. Srinivas, Programmable chemical controllers made from DNA. Nat. Nanotechnol. 8, 755–762 (2013)

    Article  CAS  Google Scholar 

  17. L. Cardelli, M. Kwiatkowska, L. Laurenti, Programming discrete distributions with chemical reaction networks. Nat. Comput. 17, 131–145 (2017)

    Article  Google Scholar 

  18. S. Shah, J. Wee, T. Song, Using strand displacing polymerase to program chemical reaction networks. J. Am. Chem. Soc. 142, 9587–9593 (2020)

    CAS  PubMed  Google Scholar 

  19. R. Brijder, Computing with chemical reaction networks: a tutorial. Nat. Comput. 18, 119–137 (2018)

    Article  Google Scholar 

  20. L. Cardelli, M. Kwiatkowska, M. Whitby, Chemical reaction network designs for asynchronous logic circuits. Nat. Comput. 17, 109–130 (2017)

    Article  Google Scholar 

  21. S. Salehi, K. Parhi, M. Riedel, Chemical reaction networks for computing polynomials. ACS Synth. Biol. 6, 76–83 (2017)

    Article  CAS  Google Scholar 

  22. T. Song, S. Garg, R. Mokhtar, Analog computation by DNA strand displacement circuits. ACS Synth. Biol. 5, 898–912 (2016)

    Article  CAS  Google Scholar 

  23. N. Paulino, M. Foo, J. Kim, On the stability of nucleic acid feedback control systems. Automatica 119, 109103 (2020)

    Article  Google Scholar 

  24. T. Nakakuki, J. Imura, Finite-time regulation property of DNA feedback regulator. Automatica 114, 108826 (2020)

    Article  Google Scholar 

  25. K. Oishi, E. Klavins, Biomolecular implementation of linear I/O systems. IET Syst. Biol. 5, 252–260 (2011)

    Article  CAS  Google Scholar 

  26. B. Yordanov, J. Kim, R. Petersen, Computational design of nucleic acid feedback control circuits. ACS Synth. Biol. 3, 600–616 (2014)

    Article  CAS  Google Scholar 

  27. R. Sawlekar, F. Montefusco, V. Kulkarni, Implementing nonlinear feedback controllers using DNA strand displacement reactions. IEEE Trans. NanoBiosci. 15, 443–454 (2016)

    Article  Google Scholar 

  28. M. Foo, J. Kim, R. Sawlekar, Design of an embedded inverse-feedforward biomolecular tracking controller for enzymatic reaction processes. Comput. Chem. Eng. 99, 145–157 (2017)

    Article  CAS  Google Scholar 

  29. N. Paulino, M. Foo, J. Kim, PID and state feedback controllers using DNA strand displacement reactions. IEEE Control Syst. Lett. 3, 805–810 (2019)

    Article  Google Scholar 

  30. M. Whitby, L. Cardelli, M. Kwiatkowska, PID control of biochemical reaction networks. IEEE Trans. Autom. Control 67(2), 1023–1030 (2022)

    Article  Google Scholar 

  31. Y. Yuan, H. Lv, Q. Zhang, DNA strand displacement reactions to accomplish a two-degree-of-freedom PID controller and its application in subtraction gate. IEEE Trans. NanoBiosci. 20(4), 554–564 (2021)

    Article  Google Scholar 

  32. R. Veillette, Reliable linear-quadratic state-feedback control. Automatica 31, 137–143 (1995)

    Article  Google Scholar 

  33. H. Zhang, F. Lewis, A. Das, Optimal design for synchronization of cooperative systems: state feedback, observer and output feedback. IEEE Trans. Autom. Control 56, 1948–1952 (2011)

    Article  Google Scholar 

  34. H. Zhang, F. Tao, H. Liang, LQR-based optimal distributed cooperative design for linear discrete-time multiagent systems. IEEE Trans. Neural Netw. Learn. Syst. 28, 599–611 (2015)

    Article  Google Scholar 

  35. A. Barrau, S. Bonnabel, Linear observed systems on groups. Syst. Control Lett. 129, 36–42 (2019)

    Article  Google Scholar 

Download references

Funding

This work is supported by the National Key Technology R&D Program of China (No. 2018YFC0910500), the National Natural Science Foundation of China (Nos. 61425002, 61751203, 61772100, 61972266, 61802040), the Natural Science Foundation of Liaoning Province (Nos. 2020-KF-14-05, 2021-KF-11-03), the High-level Talent Innovation Support Program of Dalian City (No. 2018RQ75), the State Key Laboratory of Light Alloy Casting Technology for High-end Equipment (No. LACT-006), the Innovation and Entrepreneurship Team of Dalian University (No. XQN202008) and the LiaoNing Revitalization Talents Program (No. XLYC2008017).

Author information

Authors and Affiliations

  1. Key Laboratory of Advanced Design and Intelligent Computing, Ministry of Education, School of Software Engineering, Dalian University, Dalian, 116622, Liaoning, China

    Youyang Yuan, Hui Lv & Qiang Zhang

  2. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, 110004, Liaoning, China

    Hui Lv

  3. School of Computer Science and Technology, Dalian University of Technology, Dalian, 116024, Liaoning, China

    Qiang Zhang

Authors
  1. Youyang Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hui Lv
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qiang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors have read and agreed to the published version of the manuscript. YY: Conceptualization, investigation, writing—original draft preparation; HL: writing—review and editing; QZ: funding acquisition.

Corresponding authors

Correspondence to Hui Lv or Qiang Zhang.

Ethics declarations

Conflict of interest

The authors declare no conflicts of interest.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yuan, Y., Lv, H. & Zhang, Q. Molecular device design based on chemical reaction networks: state feedback controller, static pre-filter, addition gate control system and full-dimensional state observer. J Math Chem 60, 915–935 (2022). https://doi.org/10.1007/s10910-022-01340-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-022-01340-z

Keywords

Search

Navigation