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A Stochastic Automata Network Description for Spatial DNA-Methylation Models

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Measurement, Modelling and Evaluation of Computing Systems (MMB 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12040))

Abstract

DNA methylation is an important biological mechanism to regulate gene expression and control cell development. Mechanistic modeling has become a popular approach to enhance our understanding of the dynamics of methylation pattern formation in living cells. Recent findings suggest that the methylation state of a cytosine base can be influenced by its DNA neighborhood. Therefore, it is necessary to generalize existing mathematical models that consider only one cytosine and its partner on the opposite DNA-strand (CpG), in order to include such neighborhood dependencies. One approach is to describe the system as a stochastic automata network (SAN) with functional transitions. We show that single-CpG models can successfully be generalized to multiple CpGs using the SAN description and verify the results by comparing them to results from extensive Monte-Carlo simulations.

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References

  1. Arand, J., et al.: In vivo control of CpG and non-CpG DNA methylation by DNA methyltransferases. PLoS Genet. 8(6), e1002750 (2012)

    Article  Google Scholar 

  2. Assunçao, J., Espindola, L., Fernandes, P., Pivel, M., Sales, A.: A structured stochastic model for prediction of geological stratal stacking patterns. Electron. Notes Theor. Comput. Sci. 296, 27–42 (2013)

    Article  Google Scholar 

  3. Bonello, N., et al.: Bayesian inference supports a location and neighbour-dependent model of DNA methylation propagation at the MGMT gene promoter in lung tumours. J. Theor. Biol. 336, 87–95 (2013)

    Article  Google Scholar 

  4. Buchholz, P.: Equivalence relations for stochastic automata networks. In: Stewart, W.J. (ed.) Computations with Markov Chains, pp. 197–215. Springer, Boston (1995). https://doi.org/10.1007/978-1-4615-2241-6_13

    Chapter  Google Scholar 

  5. Buchholz, P.: Hierarchical Markovian models: symmetries and reduction. Perform. Eval. 22(1), 93–110 (1995)

    Article  Google Scholar 

  6. Buchholz, P., Kemper, P.: Kronecker based matrix representations for large Markov models. In: Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P., Siegle, M. (eds.) Validation of Stochastic Systems. LNCS, vol. 2925, pp. 256–295. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24611-4_8

    Chapter  Google Scholar 

  7. Czekster, R.M., Fernandes, P., Lopes, L., Sales, A., Santos, A.R., Webber, T.: Stochastic performance analysis of global software development teams. ACM Trans. Softw. Eng. Methodol. 25(3), 1–32 (2016)

    Article  Google Scholar 

  8. Davio, M.: Kronecker products and shuffle algebra. IEEE Trans. Comput. 100(2), 116–125 (1981)

    Article  MathSciNet  Google Scholar 

  9. DeRemigio, H., Kemper, P., LaMar, M.D., Smith, G.D.: Markov chain models of coupled intracellular calcium channels: Kronecker structured representations and benchmark stationary distribution calculations. In: Biocomputing 2008, pp. 354–365. World Scientific (2008)

    Google Scholar 

  10. Fernandes, P., Plateau, B., Stewart, W.J.: Efficient descriptor-vector multiplications in stochastic automata networks. J. ACM 45(3), 381–414 (1998)

    Article  MathSciNet  Google Scholar 

  11. Fernandes, P., Sales, A., Santos, A.R., Webber, T.: Performance evaluation of software development teams: a practical case study. Electron. Notes Theor. Comput. Sci. 275, 73–92 (2011)

    Article  Google Scholar 

  12. Giehr, P., Kyriakopoulos, C., Ficz, G., Wolf, V., Walter, J.: The influence of hydroxylation on maintaining CpG methylation patterns: a hidden Markov model approach. PLoS Comput. Biol. 12(5), e1004905 (2016)

    Article  Google Scholar 

  13. Gowher, H., Jeltsch, A.: Molecular enzymology of the catalytic domains of the DNMT3A and DNMT3B DNA methyltransferases. J. Biol. Chem. 277(23), 20409–20414 (2002)

    Article  Google Scholar 

  14. Haerter, J.O., Lövkvist, C., Dodd, I.B., Sneppen, K.: Collaboration between CpG sites is needed for stable somatic inheritance of DNA methylation states. Nucleic Acids Res. 42(4), 2235–2244 (2013)

    Article  Google Scholar 

  15. Holz-Schietinger, C., Reich, N.O.: The inherent processivity of the human de novo methyltransferase 3A (DNMT3A) is enhanced by DNMT3L. J. Biol. Chem. 285(38), 29091–29100 (2010)

    Article  Google Scholar 

  16. Kyriakopoulos, C., Giehr, P., Lück, A., Walter, J., Wolf, V.: A Hybrid HMM Approach for the Dynamics of DNA Methylation. arXiv preprint arXiv:1901.06286 (2019)

    Chapter  Google Scholar 

  17. Lövkvist, C., Dodd, I.B., Sneppen, K., Haerter, J.O.: DNA methylation in human epigenomes depends on local topology of CpG sites. Nucleic Acids Res. 44(11), 5123–5132 (2016)

    Article  Google Scholar 

  18. Lück, A., Giehr, P., Nordström, K., Walter, J., Wolf, V.: Hidden Markov modelling reveals neighborhood dependence of DNMT3A and 3B activity. IEEE/ACM Trans. Comput. Biol. Bioinform. 16, 1598–1609 (2019)

    Article  Google Scholar 

  19. Lück, A., Giehr, P., Walter, J., Wolf, V.: A stochastic model for the formation of spatial methylation patterns. In: Feret, J., Koeppl, H. (eds.) CMSB 2017. LNCS, vol. 10545, pp. 160–178. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67471-1_10

    Chapter  Google Scholar 

  20. Meyer, K.N., Lacey, M.R.: Modeling methylation patterns with long read sequencing data. IEEE/ACM Trans. Comput. Biol. Bioinform. 15(4), 1379–1389 (2017)

    Article  Google Scholar 

  21. Norvil, A.B., Petell, C.J., Alabdi, L., Wu, L., Rossie, S., Gowher, H.: DNMT3B methylates DNA by a noncooperative mechanism, and its activity is unaffected by manipulations at the predicted dimer interface. Biochemistry 57(29), 4312–4324 (2016)

    Article  Google Scholar 

  22. Plateau, B., Atif, K.: Stochastic automata network of modeling parallel systems. IEEE Trans. Softw. Eng. 17(10), 1093–1108 (1991)

    Article  MathSciNet  Google Scholar 

  23. Stewart, W.J., Atif, K., Plateau, B.: The numerical solution of stochastic automata networks. Eur. J. Oper. Res. 86(3), 503–525 (1995)

    Article  Google Scholar 

  24. Wolf, V.: Modelling of biochemical reactions by stochastic automata networks. Electron. Notes Theor. Comput. Sci. 171(2), 197–208 (2007). Proceedings of the First Workshop on Membrane Computing and Biologically Inspired Process Calculi (MeCBIC 2006)

    Article  Google Scholar 

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Lück, A., Wolf, V. (2020). A Stochastic Automata Network Description for Spatial DNA-Methylation Models. In: Hermanns, H. (eds) Measurement, Modelling and Evaluation of Computing Systems. MMB 2020. Lecture Notes in Computer Science(), vol 12040. Springer, Cham. https://doi.org/10.1007/978-3-030-43024-5_4

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  • DOI: https://doi.org/10.1007/978-3-030-43024-5_4

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  • Print ISBN: 978-3-030-43023-8

  • Online ISBN: 978-3-030-43024-5

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