Abstract
We investigate the problem of finding optimal one-bit perturbation that maximizes the size of the basin of attractions (BOAs) of desired attractors and minimizes the size of the BOAs of undesired attractors for large-scale Boolean networks by cascading aggregation. First, via the aggregation, a necessary and sufficient condition is given to ensure the invariance of desired attractors after one-bit perturbation. Second, an algorithm is proposed to identify whether the one-bit perturbation will cause the emergence of new attractors or not. Next, the change of the size of BOAs after one-bit perturbation is provided in an algorithm. Finally, the efficiency of the proposed method is verified by a T-cell receptor network.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Campbell C, Albert R, 2014. Stabilization of perturbed Boolean network attractors through compensatory interactions. BMC Syst Biol, 8:53. https://doi.org/10.1186/1752-0509-8-53
Cheng DZ, Qi HS, Li ZQ, 2011. Analysis and Control of Boolean Networks: a Semi-tensor Product Approach. Springer, London, UK. https://doi.org/10.1007/978-0-85729-097-7
Ding XY, Li HT, Yang QQ, et al., 2017. Stochastic stability and stabilization of n-person random evolutionary Boolean games. Appl Math Comput, 306:1–12. https://doi.org/10.1016/j.amc.2017.02.020
Fan HB, Feng JE, Meng M, et al., 2020. General decomposition of fuzzy relations: semi-tensor product approach. Fuzzy Sets Syst, 384:75–90. https://doi.org/10.1016/j.fss.2018.12.012
Hu MX, Shen LZ, Zan XZ, et al., 2016. An efficient algorithm to identify the optimal one-bit perturbation based on the basin-of-state size of Boolean networks. Sci Rep, 6:26247. https://doi.org/10.1038/srep26247
Kauffman SA, 1969. Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol, 22(3):437–467. https://doi.org/10.1016/0022-5193(69)90015-0
Klamt S, Saez-Rodriguez J, Lindquist JA, et al., 2006. A methodology for the structural and functional analysis of signaling and regulatory networks. BMC Bioinform, 7:56. https://doi.org/10.1186/1471-2105-7-56
Li HT, Ding XY, 2019. A control Lyapunov function approach to feedback stabilization of logical control networks. SIAM J Contr Optim, 57(2):810–831. https://doi.org/10.1137/18M1170443
Li HT, Wang YZ, Liu ZB, 2012. Function perturbation impact on the topological structure of Boolean networks. Proc 10th World Con gress on Intelligent Control and Automation, p.1241–1246. https://doi.org/10.1109/WCICA.2012.6358071
Li HT, Xu XJ, Ding XY, 2019. Finite-time stability analysis of stochastic switched Boolean networks with impulsive effect. Appl Math Comput, 347:557–565. https://doi.org/10.1016/j.amc.2018.11.018
Liu JY, Liu Y, Guo YQ, et al., 2019. Sampled-data statefeedback stabilization of probabilistic Boolean control networks: a control Lyapunov function approach. IEEE Trans Cybern, in press. https://doi.org/10.1109/TCYB.2019.2932914
Liu M, 2015. Analysis and Synthesis of Boolean Networks. Licentiate Thesis, KTH School of Information and Communication Technology, Sweden.
Liu Y, Li BW, Lu JQ, et al., 2017. Pinning control for the disturbance decoupling problem of Boolean networks. IEEE Trans Autom Contr, 62(12):6595–6601. https://doi.org/10.1109/TAC.2017.2715181
Liu YS, Zheng YT, Li HT, et al., 2018. Control design for output tracking of delayed Boolean control networks. J Comput Appl Math, 327:188–195. https://doi.org/10.1016/j.cam.2017.06.016
Lu JQ, Zhong J, Huang C, et al., 2016. On pinning controllability of Boolean control networks. IEEE Trans Autom Contr, 61(6):1658–1663. https://doi.org/10.1109/TAC.2015.2478123
Lu JQ, Li HT, Liu Y, et al., 2017. Survey on semi-tensor product method with its applications in logical networks and other finite-valued systems. IET Contr Theory Appl, 11(13):2040–2047. https://doi.org/10.1049/iet-cta.2016.1659
Lu JQ, Li ML, Liu Y, et al., 2018a. Nonsingularity of Grainlike cascade FSRs via semi-tensor product. Sci China Inform Sci, 61:010204. https://doi.org/10.1007/s11432-017-9269-6
Lu JQ, Sun LJ, Liu Y, et al., 2018b. Stabilization of Boolean control networks under aperiodic sampled-data control. SIAM J Contr Optim, 56(6):4385–4404. https://doi.org/10.1137/18M1169308
Lu JQ, Li ML, Huang TW, et al., 2018c. The transformation between the Galois NLFSRs and the Fibonacci NLF-SRs via semi-tensor product of matrices. Automatica, 96:393–397. https://doi.org/10.1016/j.automatica.2018.07.011
Ostrowski M, Paulevé L, Schaub T, et al., 2016. Boolean network identification from perturbation time series data combining dynamics abstraction and logic programming. Biosystems, 149:139–153. https://doi.org/10.1016/j.biosystems.2016.07.009
Shmulevich I, Dougherty ER, Zhang W, 2002a. From Boolean to probabilistic Boolean networks as models of genetic regulatory networks. Proc IEEE, 90(11):1778–1792. https://doi.org/10.1109/JPROC.2002.804686
Shmulevich I, Dougherty ER, Zhang W, 2002b. Control of stationary behavior in probabilistic Boolean networks by means of structural intervention. JBiolSyst, 10(4):431–445. https://doi.org/10.1142/S0218339002000706
Shmulevich I, Dougherty ER, Zhang W, 2002c. Gene perturbation and intervention in probabilistic Boolean networks. Bioinformatics, 18(10):1319–1331. https://doi.org/10.1093/bioinformatics/18.10.1319
Wang B, Feng JE, 2019. On detectability of probabilistic Boolean networks. Inform Sci, 483:383–395. https://doi.org/10.1016/j.ins.2019.01.055
Wang B, Feng JE, Meng M, 2019. Model matching of switched asynchronous sequential machines via matrix approach. Int J Contr, 92(10):2430–2440. https://doi.org/10.1080/00207179.2018.1441552
Xiao YF, Dougherty ER, 2007. The impact of function perturbations in Boolean networks. Bioinformatics, 23(10):1265–1273. https://doi.org/10.1093/bioinformatics/btm093
Xu XJ, Li HT, Li YL, et al., 2018. Output tracking control of Boolean control networks with impulsive effects. Math Methods Appl Sci, 41(4):1554–1564. https://doi.org/10.1002/mma.4685
Yu YY, Feng JE, Pan JF, et al., 2019a. Block decoupling of Boolean control networks. IEEE Trans Autom Contr, 64(8):3129–3140. https://doi.org/10.1109/TAC.2018.2880411
Yu YY, Wang B, Feng JE, 2019b. Input observability of Boolean control networks. Neurocomputing, 333:22–28. https://doi.org/10.1016/j.neucom.2018.12.014
Zhang LQ, Feng JE, Feng XH, et al., 2014. Further results on disturbance decoupling of mix-valued logical networks. IEEE Trans Autom Contr, 59(6):1630–1634. https://doi.org/10.1109/TAC.2013.2292733
Zhao Y, Kim J, Filippone M, 2013. Aggregation algorithm towards large-scale Boolean network analysis. IEEE Trans Autom Contr, 58(8):1976–1985. https://doi.org/10.1109/TAC.2013.2251819
Zhao Y, Ghosh BK, Cheng DZ, 2016. Control of large-scale Boolean networks via network aggregation. IEEE Trans Neur Netw Learn Syst, 27(7):1527–1536. https://doi.org/10.1109/TNNLS.2015.2442593
Zhong J, Li BW, Liu Y, et al., 2020. Output feedback stabilizer design of Boolean networks based on network structure. Front Inform Technol Electron Eng, 21(2):247–259. https://doi.org/10.1631/FITEE.1900229
Zhu QX, Liu Y, Lu JQ, et al., 2018. On the optimal control of Boolean control networks. SIAM J Contr Optim, 56(2):1321–1341. https://doi.org/10.1137/16M1070281
Author information
Authors and Affiliations
Contributions
Jin-feng PAN designed the research, processed the data, and drafted the manuscript. Min MENG helped organize the manuscript. Jin-feng PAN revised and finalized the manuscript.
Corresponding author
Additional information
Compliance with ethics guidelines
Jin-feng PAN and Min MENG declare that they have no conflict of interest.
Project supported by the National Natural Science Foundation of China (No. 61773371)
Rights and permissions
About this article
Cite this article
Pan, Jf., Meng, M. Optimal one-bit perturbation in Boolean networks based on cascading aggregation. Front Inform Technol Electron Eng 21, 294–303 (2020). https://doi.org/10.1631/FITEE.1900411
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/FITEE.1900411