# Sequential Reprogramming of Biological Network Fate

## Abstract

A major challenge in precision medicine consists in finding the appropriate network rewiring to induce a particular reprogramming of the cell phenotype. The rewiring is caused by specific network action either inhibiting or over-expressing targeted molecules. In some cases, a therapy abides by a time-scheduled drug administration protocol. Furthermore, some diseases are induced by a sequence of mutations leading to a sequence of actions on molecules. In this paper, we extend previous works on abductive-based inference of network reprogramming [3] by investigating the sequential control of Boolean networks. We present a novel theoretical framework and give an upper bound on the size of control sequences as a function of the number of observed variables. We also define an algorithm for inferring minimal parsimonious control sequences allowing to reach a final state satisfying a particular phenotypic property.

## Keywords

Dynamical systems reprogramming Boolean Control Network Control sequence Abductive reasoning Drug target prediction Sequential therapy## References

- 1.Barabási, A.-L., Gulbahce, N., Loscalzo, J.: Network medicine: a network-based approach to human disease. Nat. Rev. Genet.
**12**, 56–68 (2011)CrossRefGoogle Scholar - 2.Biane, C., Delaplace, F.: Abduction based drug target discovery using Boolean control network. In: Feret, J., Koeppl, H. (eds.) CMSB 2017. LNCS, vol. 10545, pp. 57–73. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67471-1_4CrossRefGoogle Scholar
- 3.Biane, C., Delaplace, F.: Causal reasoning on Boolean control networks based on abduction: theory and application to cancer drug discovery. IEEE/ACM Trans. Comput. Biol. Bioinf. (2018). (Epub ahead of print)Google Scholar
- 4.Burga, L.N., et al.: Loss of BRCA1 leads to an increase in epidermal growth factor receptor expression in mammary epithelial cells, and epidermal growth factor receptor inhibition prevents estrogen receptor-negative cancers in BRCA1-mutant mice. Breast Cancer Res.
**13**(2), R30 (2011)CrossRefGoogle Scholar - 5.Chau, C.H., Rixe, O., McLeod, H., Figg, W.D.: Validation of analytic methods for biomarkers used in drug development. Clin. Cancer Res.
**14**(19), 5967–5976 (2008)CrossRefGoogle Scholar - 6.Cheng, A., Esparza, J., Palsberg, J.: Complexity results for 1-safe nets. Theoret. Comput. Sci.
**147**(1), 117–136 (1995)MathSciNetCrossRefGoogle Scholar - 7.Creixell, P., et al.: Kinome-wide decoding of network-attacking mutations rewiring cancer signaling. Cell
**163**(1), 202–217 (2015)MathSciNetCrossRefGoogle Scholar - 8.Csermely, P., Korcsmàros, T., Kiss, H.J.M., London, G., Nussinov, R.: Structure and dynamics of molecular networks: a novel paradigm of drug discovery: a comprehensive review. Pharmacol. Ther.
**138**(3), 333–408 (2013)CrossRefGoogle Scholar - 9.Fearon, E.R., Vogelstein, B.: A genetic model for colorectal tumorigenesis. Cell
**61**(5), 759–767 (1990)CrossRefGoogle Scholar - 10.Garey, M.R., Johnson, D.S.: Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1990)zbMATHGoogle Scholar
- 11.Lee, M., et al.: Sequential application of anti-cancer drugs enhances cell death by re-wiring apoptotic signaling networks. Cell
**149**, 780–794 (2012)CrossRefGoogle Scholar - 12.Lin, P.-C.K., Khatri, S.P.: Application of Max-SAT-based ATPG to optimal cancer therapy design. BMC Genom.
**13 Suppl 6**(Suppl. 6), S5 (2012)CrossRefGoogle Scholar - 13.Mandon, H., Haar, S., Paulevé, L.: Temporal reprogramming of Boolean networks. In: Feret, J., Koeppl, H. (eds.) CMSB 2017. LNCS, vol. 10545, pp. 179–195. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67471-1_11CrossRefGoogle Scholar
- 14.Mandon, H., Su, C., Pang, J., Paul, S., Haar, S., Paulevé, L.: Algorithms for the sequential reprogramming of Boolean networks. IEEE/ACM Trans. Comput. Biol. Bioinf. (2019 to appear)Google Scholar
- 15.Murrugarra, D., Veliz-Cuba, A., Aguilar, B., Laubenbacher, R.: Identification of control targets in Boolean molecular network models via computational algebra. BMC Syst. Biol.
**10**(1), 94 (2016)CrossRefGoogle Scholar - 16.Sahni, N., et al.: Edgotype: a fundamental link between genotype and phenotype. Curr. Opin. Genet. Dev.
**23**(6), 649–657 (2013)CrossRefGoogle Scholar - 17.Strimbu, K., Tavel, J.A.: What are Biomarkers? Curr. Opin. HIV AIDS
**5**(6), 463–466 (2011)CrossRefGoogle Scholar - 18.Vogel, G.: Reprogramming cells. Science
**322**(5909), 1766–1767 (2008)CrossRefGoogle Scholar - 19.Zanudo, J.G.T., Albert, R.: Cell fate reprogramming by control of intracellular network dynamics. PLoS Comput. Biol.
**11**(4), e1004193 (2015)CrossRefGoogle Scholar - 20.Zhong, Q., et al.: Edgetic perturbation models of human inherited disorders. Mol. Syst. Biol.
**5**(321), 321 (2009)CrossRefGoogle Scholar