Abstract
DNA specific fragments are required in DNA computing. The fragments are usually obtained through DNA catalytic reactions. For achieving accurate regulation of DNA catalytic reaction network, toehold has been added into it. Due to the inevitable transcriptions and translations of DNA strands, the outcome of DNA catalytic reaction network using toehold may be affected by these operational delays. Based on this, a nonlinear differential model of complex DNA catalytic reaction network using toehold is proposed. Double time delays characterize delays of two DNA strands transcription in the reaction process. By assigning reactant concentrations and reaction rates, the stability of complex DNA catalytic reaction network system with double time delays is analyzed. The Hopf bifurcation at the equilibrium point is studied and the results of mathematical analysis are obtained. Finally, the correctness of theoretical analysis is verified by numerical simulation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Adleman, L.: Molecular computation of solutions to combinatorial problems. Science 266(5187), 1021–1024 (1994)
Yurke, B., Turberfield, A., Mills, A., Simmel, F., Neumann, J.: A DNA-fuelled molecular machine made of DNA. Nature 406, 605–608 (2000)
Zadegan, R., Jepsen, M., Hildebrandt, L., Birkedal, V., Kjems, J.: Construction of a fuzzy and Boolean logic gates based on DNA. Small 11(15), 1811–1817 (2015)
Andrianova, M., Kuznetsov, A.: Logic Gates Based on DNA Aptamers. Pharmaceuticals 13(11), 417 (2020)
Sami, P., Shen, C., Sani, M.: Ultra-fast all optical half-adder realized by combining AND/XOR logical gates using a nonlinear nanoring resonator. Appl. Opt. 59(22), 6459–6465 (2020)
Wang, Z., Ren, X., Ji, Z., Huang, W., Wu, T.: A novel bio-heuristic computing algorithm to solve the capacitated vehicle routing problem based on Adleman-Lipton model. Biosystems 184, 103997–104006 (2019)
Tian, X., Liu, X., Zhang, H., Sun, M., Zhao, Y.: A DNA algorithm for the job shop scheduling problem based on the Adleman-Lipton model. PLoS ONE 15, e0242083 (2020)
Song, B., Zhang, Y., Park, J., Yang, Z.: Delay-dependent stability analysis of stochastic time-delay systems involving Poisson process. J. Franklin Inst. 358(1), 1087–1102 (2021)
Kaslik, E., Neamţu, M., Vesa, L.: Global stability analysis of an unemployment model with distributed delay. Math. Comput. Simul. 185(4), 535–546 (2021)
Cai, T., Cheng, P.: Stability Analysis of discrete-time stochastic delay systems with impulses. Mathematics 9, 418 (2021)
Zhang, X., Wang, Y., Wu, L.: Analysis and design of delayed genetic regulatory networks. Studies in Systems, Decision and Control 2019, pp. 57-80. Springer, Warsaw (2017). https://doi.org/10.1007/978-3-030-17098-1
Abdulrashid, I.A.M., Han, X.: Stability analysis of a chemotherapy model with delays. Discrete Continuous Dyn. Syst. - B 24(3), 989–1005 (2019)
Wang, J.-A., Fan, L., Wen, X.-Y.: Improved Results on Stability Analysis for Delayed Neural Network. Int. J. Control Autom. Syst. 18(7), 1853–1862 (2020). https://doi.org/10.1007/s12555-019-0536-0
Elaiw, A., Alshehaiween, S., Hobiny, A.: Global properties of a delay-distributed HIV dynamics model including impairment of B-Cell functions. Mathematics 7(9), 837 (2019)
Khajanchi, S.: Chaotic dynamics of a delayed tumor–immune interaction model. Int. J. Biomathematics 13(5), 2050009 (2020)
Prakash, M., Rakkiyappan, R., Manivannan, A., Cao, J.: Dynamical analysis of antigen-driven T-cell infection model with multiple delays. Appl. Math. Comput. 354, 266–281 (2019)
Xie, B., Xu, F.: Stability analysis for a time-delayed nonlinear predator–prey model. Adv. Difference Equ. 2018(1), 1–16 (2018). https://doi.org/10.1186/s13662-018-1564-4
Du, Y., Niu, B., Wei, J.: Two delays induce Hopf bifurcation and double Hopf bifurcation in a diffusive Leslie-Gower predator-prey system. Chaos 29(1), 013101 (2019)
Yin, Z., Yu, Y., Lu, Z.: Stability analysis of an age-structured SEIRS model with time delay. Mathematics 8(3), 455 (2020)
Zhang, D., Winfree, E.: Control of DNA strand displacement kinetics using toehold exchange. J. Am. Chem. Soc. 131(47), 17303–17314 (2009)
Acknowledgements
This work is supported by the National Key R&D Program of China (No. 2018YFC0910500), National Natural Science Foundation of China (Nos. 61425002, 61751203, 61772100, 61972266, 61802040, 61672121, 61572093), Program for Changjiang Scholars and Innovative Research Team in University (No. IRT_15R07), Program for Liaoning Innovative Research Team in University (No. LT2017012), Natural Science Foundation of Liaoning Province (Nos. 2020-KF-14–05, 2019-ZD-0567), High-level Talent Innovation Support Program of Dalian City (Nos. 2017RQ060, 2018RQ75), Dalian Outstanding Young Science and Technology Talent Support Program (No. 2017RJ08), State Key Laboratory of Light Alloy Casting Technology for High-end Equipment (No.LACT-006) and Scientific Research Fund of Liaoning Provincial Education Department (No. JYT19051).
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Chen, W., Lv, H., Zhang, Q. (2021). Stability and Hopf Bifurcation Analysis of Complex DNA Catalytic Reaction Network with Double Time Delays. In: Tan, Y., Shi, Y. (eds) Advances in Swarm Intelligence. ICSI 2021. Lecture Notes in Computer Science(), vol 12689. Springer, Cham. https://doi.org/10.1007/978-3-030-78743-1_51
Download citation
DOI: https://doi.org/10.1007/978-3-030-78743-1_51
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-78742-4
Online ISBN: 978-3-030-78743-1
eBook Packages: Computer ScienceComputer Science (R0)