A case study of the sensitivity and topology of nodes of reduced Boolean networks

Document Type : Original Paper

Author

faculty of mathematical sciences. Tarbiat modares, Tehran.

Abstract

Boolean networks are one of the models for studying complex dynamic behaviors in biological systems. The analysis of attractors of these networks is very important .But the exponential dependence of the state transition graph of these models with the number of network nodes is a major problem for large-scale systems analysis. Therefore, it is necessary to use network reduction methods. In these methods, the size of the networks is reduced, while the dynamic properties are preserved, but the reduction methods are not minimal. In this paper, while the two biological networks "abscisic acid" and "breast cancer" have been reduced, also the sensitivity analysis of the nodes of the reduced networks has been performed. The results show that reduced network nodes are important components in the main network dynamics because most of them have zero opposite sensitivity. Also, zero sensitivity nodes in reduced networks can be removed under certain conditions, using From the reduction method and the concept of sensitivity, our proposed method is able to modify the Saadatpour reduction method. Using the proposed method, we obtained reduced networks with fewer nodes that maintain the main network dynamics and have a smaller state space. These nodes are also important in both structural and dynamic aspects of biological networks.

Keywords

Main Subjects


[1] Barrat, A. Barthelemy, M. and Vespignani, Dynamical processes on complex networks, Cambridge
university press, 2008.
[2] Biane, C. Delaplace, F. and Klaudel, H, Networks and games for precision medicine, Biosystems.
150 (2016) 52-60.
[3] Ghanbarnejad, F. and Klemm, K, Impact of individual nodes in Boolean network dynamics, EPL
(Europhysics Letters). 99(5) (2012) 58-69.
[4] Gomperts, B. D. and Tatham, P. E, Signal transduction, Academic Press, 2009.
[5] Gordon, K. J. and Blobe, G. C, Role of transforming growth factor-β superfamily signaling pathways
in human disease, Biochimica et Biophysica Acta (BBA)-Molecular Basis of Disease. 1782(4) (2008)
197-228.
[6] Ikushima, H. and Miyazono, K, TGFβ signalling: a complex web in cancer progression, Nature
reviews cancer. 10(6) (2010) 415-424.
[7] Kauffman, S. A, Metabolic stability and epigenesis in randomly constructed genetic nets, Journal of
theoretical biology. 22(3) (1969) 437-467.
[8] Kavousi, K. and Hamidi Zahedani, A. R, Reduction and Finding of Attractors in ABA Signaling
Pathway Network by Boolean Modeling, Modares Journal of Biotechnology. 10(3) (2019) 363-371.
[9] Kim, J. Vandamme, D. Kim, J. R. Munoz, A. G. Kolch, W. and Cho, K. H, Robustness and evolvability
of the human signaling network, PLoS Comput Biol. 10(7) (2014) 375-398.
[10] Little, J. W. Shepley, D. P. and Wert, D. W, Robustness of a gene regulatory circuit, The EMBO
journal. 18(15) (1999) 4299-4307.
[11] Naldi, A. Remy, E. Thieffry, D. and Chaouiya, C, Dynamically consistent reduction of logical regulatory
graphs, Theoretical Computer Science, 412(21) (2011) 2207-2218.
[12] Robeva, R. (Ed), Algebraic and discrete mathematical methods for modern biology, Academic Press,
2015.
[13] Richardson, K. A, Simplifying boolean networks, Advances in Complex Systems. 8(04) (2005) 365-
381.
[14] Saadatpour, A. Albert, I. and Albert, R, Attractor analysis of asynchronous Boolean models of signal
transduction networks, Journal of theoretical biology. 266(4) (2010) 641-656.
[15] Saadatpour, A. Albert, R. and Reluga, T. C, A reduction method for Boolean network models proven
to conserve attractors, SIAM Journal on Applied Dynamical Systems. 12(4) (2013) 1997-2011.
[16] Shreif, Z. and Periwal, V, A network characteristic that correlates environmental and genetic robustness,
PLoS Comput Biol. 10(2) (2014) 347-360.
[17] Trinh, H. C. and Kwon, Y. K, Edge-based sensitivity analysis of signaling networks by using Boolean
dynamics, Bioinformatics. 32(17) (2016) i763-i771.
[18] Veliz-Cuba, A, Reduction of Boolean network models, Journal of theoretical biology, 289 (2011)
167-172.
[١٩ ] سپیده صحرائی، مهدی میرزائی، بررسی موردی ارتباط میان دینامیک و توپولوژی شبکه های زیستی با استفاده از مدل سازی بولی 
.٣۶۴ -٣۵٣ ( کاهش یافته، چهارمین کنفرانس بین المللی ترکیبیات، رمزنگاری، علوم کامپیوتر و محاسبات. ( ١٣٩٨

Articles in Press, Accepted Manuscript
Available Online from 07 May 2022
  • Receive Date: 05 October 2020
  • Revise Date: 03 April 2022
  • Accept Date: 24 April 2022
  • First Publish Date: 07 May 2022