Abstract
DNA molecular technology has gradually matured and has been widely used in the design of nanomaterials and chemical oscillators. In order to ensure the correct setting of DNA molecular oscillator, it is necessary to thoroughly study the dynamic behavior of system. This paper studies the dynamics system of DNA molecular oscillator based on DNA strand displacement. Modeling the reaction process transforms the reaction process into a specific mathematical model. The research results show that the influence of time delay is not considered in an ideal state. Stability near the equilibrium point of system is determined by initial reaction substrate concentration and reaction rate. Considering the time delay of separation of DNA double-stranded molecules in the reaction process, the time delay parameter is added to the system model. As the time delay increases, the system changes from a stable state to an unstable state and Hopf bifurcation occurs. At the same time, the study found that both Hopf bifurcation direction and the periodic solution are closely related to the time delay parameter. The result of numerical simulation proves the correctness of our conclusion.
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
Yun, J., Cho, K., et al.: Dynamic electrical characteristics of low-power ring oscillators constructed with inorganic nanoparticles on flexible plastics. ACS Appl. Mater. Interfaces 87(19), 3725–3728 (2012)
Kitagaki, B.T., et al.: Multivariate statistical analysis of chemical and electrochemical oscillators for an accurate frequency selection. Phys. Chem. Chem. Phys. 21(30), 16423–16434 (2019)
Kim, W.J., et al.: DNA strand exchange stimulated by spontaneous complex formation with cationic comb-type copolymer. J. Am. Chem. Soc. 124(43), 12676–12677 (2002)
Zhu, E., et al.: Biochemical logic circuits based on DNA combinatorial displacement. IEEE Access 8, 34096–34103 (2020)
Wang, Y., Li, Z., et al.: Three-variable chaotic oscillatory system based on DNA strand displacement and its coupling combination synchronization. IEEE Trans. Nanobiosci. 19(3), 434–445 (2020)
Zhang, D.Y., Winfree, E.: Control of DNA strand displacement kinetics using toehold exchange. J. Am. Chem. Soc. 131(47), 17303–17314 (2009)
Haley, N.E.C., Ouldridge, T.E., et al.: Design of hidden thermodynamic driving for non-equilibrium systems via mismatch elimination during DNA strand displacement. Nat. Commun. 11(1), 1–11 (2020)
Paulino, N.M.G., Foo, M., et al.: PID and state feedback controllers using DNA strand displacement reactions. IEEE Control Syst. Lett. 3(4), 805–810 (2019)
Chen, R.P., Blackstock, D., et al.: Dynamic protein assembly by programmable DNA strand displacement. Nat. Chem. 10(4), 474–481 (2018)
Surana, S., Shenoy, A.R., et al.: Designing DNA nanodevices for compatibility with the immune system of higher organisms. Nat. Nanotechnol. 10(9), 741–747 (2015)
Zhao, J., Gao, J., et al.: Upconversion Luminescence-Activated DNA nanodevice for ATP sensing in living cells. J. Am. Chem. Soc. 140(2), 578–581 (2018)
Ali, K.K., Cattani, C., et al.: Analytical and numerical study of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model. Chaos, Solitons Fractals 139, 110089 (2020)
Srinivas, N., Parkin, J., Seelig, G., et al.: Enzyme-free nucleic acid dynamical systems. Science 358(6369), eaal2052 (2017)
Eskov, V.V., Filatova, D.Y., et al.: Classification of uncertainties in modeling of complex biological systems. Mosc. Univ. Phys. Bull. 74(1), 57–63 (2019)
Shu, Y., Huang, J., Dong, Y., et al.: Mathematical modeling and bifurcation analysis of pro-and anti-tumor macrophages. Appl. Math. Model. 88, 758–773 (2020)
Guo, Q., Sun, Z., et al.: Bifurcations in a fractional birhythmic biological system with time delay. Commun. Nonlinear Sci. Numer. Simul. 72, 318–328 (2019)
Qi, W., Kao, Y., et al.: Controller design for time-delay system with stochastic disturbance and actuator saturation via a new criterion. Appl. Math. Comput. 320, 535–546 (2018)
Huang, C., Zhang, H., Cao, J., et al.: Stability and Hopf bifurcation of a delayed prey–predator model with disease in the predator. Int. J. Bifurcat. Chaos 29(07), 1950091 (2019)
Acknowledgments
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
Sun, T., Lv, H., Zhang, Q. (2021). Stability and Hopf Bifurcation Analysis of DNA Molecular Oscillator System Based on DNA Strand Displacement. 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_48
Download citation
DOI: https://doi.org/10.1007/978-3-030-78743-1_48
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)