State regulation for complex biological networks based on dynamic optimization algorithms_Journal of Biomedical Engineering

Authors：

JIE Hao , YUAN Meichen , ZHU Guozhu ,  HONG Weirong

College of Energy Engineering, Zhejiang University, Hangzhou 310027, P.R.China;

Corresponding author：

HONG Weirong, Email: hongwr@zju.edu.cn

Keywords：

gene regulatory networks; state regulation; dynamic optimization; optimal control strategy

DOI：

10.7507/1001-5515.201810008

Video：

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Recent studies showed that certain drugs can change regulatory reaction parameters in gene regulatory networks (GRNs) and therefore restore pathological cells to a normal state. A state control framework for regulating biological networks has been built based on attractors and bifurcation theory to analyze this phenomenon. However, the control signal is self-developed in this framework, of which the parameter perturbation method can only calculate the state transition time of cells with single control variable. Therefore, an optimal control method based on the dynamic optimization algorithms is proposed for complex biological networks modeled by nonlinear ordinary differential equations (ODEs). In this approach, dynamic optimization problems are constructed based on basic characteristics of the biological networks. Furthermore, using an example of a simple low-dimensional three-node GRN and a complex high-dimensional cancer GRN, MATLAB is utilized to calculate optimal control strategies with either single or multiple control variables. This method aims to achieve accurate and rapid state regulation for biological networks, which can provide a reference for experimental researches and medical treatment.

Citation： JIE Hao, YUAN Meichen, ZHU Guozhu, HONG Weirong. State regulation for complex biological networks based on dynamic optimization algorithms. Journal of Biomedical Engineering, 2020, 37(1): 19-26. doi: 10.7507/1001-5515.201810008 Copy

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8.	de Jong H. Modeling and simulation of genetic regulatory systems: a literature review. J Comput Biol, 2002, 9(1): 67-103.
9.	柳伟伟, 贺佳, 吴骋, 等. 微分方程模型在基因调控网络构建中的应用. 中国卫生统计, 2008, 25(1): 91-96.
10.	Santillan M. On the use of the hill functions in mathematical models of gene regulatory networks. Math Model Nat Phenom, 2008, 3(2): 85-97.
11.	Huang Sui, Ernberg I, Kauffman S. Cancer attractors: a systems view of tumors from a gene network dynamics and developmental perspective. Semin Cell Dev Biol, 2009, 20(7): 869-876.
12.	Zhao Boyang, Hemann M T, Lauffenburger D A. Intratumor heterogeneity alters most effective drugs in designed combinations. Proc Natl Acad Sci U S A, 2014, 111(29): 10773-10778.
13.	陆启韶. 分岔与奇异性. 上海: 上海科技教育出版社, 1995.
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15.	洪伟荣. 大规模动态过程优化的拟序贯算法研究. 杭州: 浙江大学, 2005.
16.	Hong W R, Wang S Q, Li P, et al. A quasi-sequential approach to large-scale dynamic optimization problems. AIChE Journal, 2006, 52(1): 255-268.
17.	Hairer E, Wanner G. Solving ordinary differential equations II: stiff and differential-algebraic problems. 2nd ed. New York: Springer, 1996.
18.	袁亚湘. 非线性优化计算方法. 北京: 科学出版社, 2008.
19.	Yuan Meichen, Hong Weirong, Li Pu. Identification of optimal strategies for state transition of complex biological networks. Biochem Soc Trans, 2017, 45(4): 1015-1024.
20.	Li Chunhe, Wang Jin. Quantifying the underlying landscape and paths of cancer. Journal of the Royal Society Interface, 2014, 11(10): 20140774.

1. Emmert-Streib F, Dehmer M, Haibe-Kains B. Gene regulatory networks and their applications: understanding biological and medical problems in terms of networks. Frontiers in cell and developmental biology, 2014, 2: 38.
2. Bouaynaya N, Shterenberg R, Schonfeld D. Inverse perturbation for optimal intervention in gene regulatory networks. Bioinformatics, 2011, 27(1): 103-110.
3. Pal R, Datta A, Dougherty E R. Optimal infinite-horizon control for probabilistic boolean networks. IEEE Transactions on Signal Processing, 2006, 54(6): 2375-2387.
4. Liu Yangyu, Slotine J J, Barabási A L. Controllability of complex networks. Nature, 2011, 473(7346): 167-173.
5. Wang Lezhi, Su Riqi, Huang Zigang, et al. A geometrical approach to control and controllability of nonlinear dynamical networks. Nat Commun, 2016, 7: 11323.
6. Klickstein I, Shirin A, Sorrentino F. Energy scaling of targeted optimal control of complex networks. Nat Commun, 2017, 8: 15145.
7. Jin Suoqin, Wu Fangxiang, Zou Xiufen. Domain control of nonlinear networked systems and applications to complex disease networks. Discrete Continuous Dyn Syst Ser B, 2017, 22(6): 2169-2206.
8. de Jong H. Modeling and simulation of genetic regulatory systems: a literature review. J Comput Biol, 2002, 9(1): 67-103.
9. 柳伟伟, 贺佳, 吴骋, 等. 微分方程模型在基因调控网络构建中的应用. 中国卫生统计, 2008, 25(1): 91-96.
10. Santillan M. On the use of the hill functions in mathematical models of gene regulatory networks. Math Model Nat Phenom, 2008, 3(2): 85-97.
11. Huang Sui, Ernberg I, Kauffman S. Cancer attractors: a systems view of tumors from a gene network dynamics and developmental perspective. Semin Cell Dev Biol, 2009, 20(7): 869-876.
12. Zhao Boyang, Hemann M T, Lauffenburger D A. Intratumor heterogeneity alters most effective drugs in designed combinations. Proc Natl Acad Sci U S A, 2014, 111(29): 10773-10778.
13. 陆启韶. 分岔与奇异性. 上海: 上海科技教育出版社, 1995.
14. Biegler L T, Grossmann I E. Retrospective on optimization. Comput Chem Eng, 2004, 28(8): 1169-1192.
15. 洪伟荣. 大规模动态过程优化的拟序贯算法研究. 杭州: 浙江大学, 2005.
16. Hong W R, Wang S Q, Li P, et al. A quasi-sequential approach to large-scale dynamic optimization problems. AIChE Journal, 2006, 52(1): 255-268.
17. Hairer E, Wanner G. Solving ordinary differential equations II: stiff and differential-algebraic problems. 2nd ed. New York: Springer, 1996.
18. 袁亚湘. 非线性优化计算方法. 北京: 科学出版社, 2008.
19. Yuan Meichen, Hong Weirong, Li Pu. Identification of optimal strategies for state transition of complex biological networks. Biochem Soc Trans, 2017, 45(4): 1015-1024.
20. Li Chunhe, Wang Jin. Quantifying the underlying landscape and paths of cancer. Journal of the Royal Society Interface, 2014, 11(10): 20140774.

Journal of Biomedical Engineering

State regulation for complex biological networks based on dynamic optimization algorithms

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