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Reduced Models of Gene Regulatory Networks: Visualising Multi-modal Landscapes

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Metaheuristics for Finding Multiple Solutions

Part of the book series: Natural Computing Series ((NCS))

Abstract

We present a prototypical multimodal optimisation problem from the systems biology domain—tuning the kinetic parameters of a reduced order gene regulatory network (GRN) model to obtain optimal fits to gene expression timeseries. After introducing the problem, the chapter then illustrates different fitness landscapes of the GRN parameter fitting problem using various statistical plots of landscape features, along with local optima networks (LONs)—graphs representing local optima (modes), their basin sizes and connectivity across the landscape. In a typical multimodal optimisation process, the problem owners get presented with a putative list of modal solutions from which to verify and select a design. We argue in this chapter that it is often useful to present a characterisation of the search landscape itself along with the list of modal solutions. The characterisation of the search landscape can provide insight into the domain, and may guide, for instance, problem reformulations, or the final mode selection based on broader features than simply mode performance, e.g. basin size if robustness of modes is a concern.

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Notes

  1. 1.

    This definition of vertex has been extended to account for neutrality in the search space [32].

  2. 2.

    All figures are available in high quality under http://pop-project.ex.ac.uk/grn_lons.html.

References

  1. Adams, R., Clark, A., Yamaguchi, A., Hanlon, N., Tsorman, N., Ali, S., Lebedeva, G., Goltsov, A., Sorokin, A.A., Akman, O.E., Troein, C., Millar, A.J., Goryanin, I., Gilmore, S.: SBSI: an extensible distributed software infrastructure for parameter estimation in systems biology. Bioinformatics 29(5), 664–665 (2013)

    Article  Google Scholar 

  2. Akman, O.E., Fieldsend, J.E.: Multi-objective optimisation of gene regulatory networks: insights from a boolean circadian clock model. In: Proceedings of the 12th International Conference on Bioinformatics and Computational Biology, vol. 70, pp. 149–162 (2020)

    Google Scholar 

  3. Akman, O.E., Locke, J.C.W., Tang, S., Carré, I., Millar, A.J., Rand, D.A.: Isoform switching facilitates period control in the Neurospora crassa circadian clock. Mol. Syst. Biol. 4, 64 (2008)

    Article  Google Scholar 

  4. Akman, O.E., Rand, D.A., Brown, P.E., Millar, A.J.: Robustness from flexibility in the fungal circadian clock. BMC Syst. Biol. 4, 88 (2010)

    Article  Google Scholar 

  5. Akman, O.E., Watterson, S., Parton, A., Binns, N., Millar, A.J., Ghazal, P.: Digital clocks: simple Boolean models can quantitatively describe circadian systems. J. Roy. Soc. Interface 9(74), 2365–2382 (2012)

    Article  Google Scholar 

  6. Alyahya, K.: Fitness landscape analysis of a class of NP-hard problems. Ph.D. thesis, University of Birmingham, July (2016)

    Google Scholar 

  7. Alyahya, K., Rowe, J.E.: Simple random sampling estimation of the number of local optima. In: Handl, J., Hart, E., Lewis, P.R., López-Ibáñez, M., Ochoa, G., Paechter, B. (eds.) Parallel Problem Solving from Nature - PPSN XIV, pp. 932–941. Springer International Publishing, Cham (2016)

    Chapter  Google Scholar 

  8. Alyahya, K., Rowe, J.E.: Landscape analysis of a class of NP-hard binary packing problems. Evol. Comput. 27(1), 47–73 (2019)

    Article  Google Scholar 

  9. Banga, J.R.: Optimization in computational systems biology. BMC Syst. Biol. 2, 47 (2008)

    Article  Google Scholar 

  10. Belkhir, N., Dréo, J., Savéant, P., Schoenauer, M.: Per instance algorithm configuration of cma-es with limited budget. In: Proceedings of the Genetic and Evolutionary Computation Conference, GECCO ’17, pp. 681–688. ACM, New York, NY, USA (2017)

    Google Scholar 

  11. Breukelaar, R., Bäck, T.: Using a genetic algorithm to evolve behavior in multi dimensional cellular automata: emergence of behavior. In: Proceedings of the 7th Annual Conference on Genetic and Evolutionary Computation, GECCO ’05, pp. 107–114. ACM, New York, NY, USA (2005)

    Google Scholar 

  12. Daniels, B.C., Chen, Y.-J., Sethna, J.P., Gutenkunst, R.N., Myers, C.R.: Sloppiness, robustness, and evolvability in systems biology. Curr. Opin. Biotechnol. 19(4), 389–395 (2008). Protein technologies/Systems biology

    Google Scholar 

  13. de Jong, H.: Modeling and simulation of genetic regulatory systems: a literature review. J. Comput. Biol. 9(1), 67–103 (2002). PMID: 11911796

    Article  MathSciNet  Google Scholar 

  14. Dee, D.P., Ghil, M.: Boolean difference equations, i: formulation and dynamic behavior. SIAM J. Appl. Math. 44(1), 111–126 (1984)

    Article  MathSciNet  Google Scholar 

  15. Doherty, K., Alyahya, K., Akman, O.E., Fieldsend, J.E.: Optimisation and landscape analysis of computational biology models: a case study. In: Proceedings of the Genetic and Evolutionary Computation Conference Companion, GECCO ’17, pp. 1644–1651. ACM, New York, NY, USA (2017)

    Google Scholar 

  16. Doye, J.P.K.: Network topology of a potential energy landscape: a static scale-free network. Phys. Rev. Lett. 88, 23:238701 (2002)

    Article  Google Scholar 

  17. Foo, M., Bates, D.G., Akman, O.E.: A simplified modelling framework facilitates more complex representations of plant circadian clocks. PLoS Comput. Biol. 16(3), e1007671 (2020)

    Google Scholar 

  18. Ghil, M., Zaliapin, I., Coluzzi, B.: Boolean delay equations: a simple way of looking at complex systems. Phys. D: Nonlinear Phenom. 237(23), 2967–2986 (2008)

    Article  MathSciNet  Google Scholar 

  19. Gutenkunst, R.N., Waterfall, J.J., Casey, F.P., Brown, K.S., Myers, C.R., Sethna, J.P.: Universally sloppy parameter sensitivities in systems biology models. PLoS Comput. Biol. 3(10), e189 (2007)

    Google Scholar 

  20. Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolution strategies. Evol. Comput. 9(2), 159–195 (2001)

    Article  Google Scholar 

  21. Hoos, H.H., Stützle, T.: Stochastic Local Search: Foundations and Applications. Elsevier (2004)

    Google Scholar 

  22. Kauffman, S., Weinberger, E.: The NK model of rugged fitness landscapes and its application to the maturation of the immune response. J. Theor. Biol. 141(2), 211–245 (1989)

    Article  Google Scholar 

  23. Leloup, J.C., Gonze, D., Goldbeter, A.: Limit cycle models for circadian rhythms based on transcriptional regulation in Drosophila and Neurospora. J. Biol. Rhythms 14(6), 433–448 (1999)

    Article  Google Scholar 

  24. Ochoa, G., Tomassini, M., Vérel, S., Darabos, C.: A study of NK landscapes’ basins and local optima networks. In: Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation, pp. 555–562. ACM (2008)

    Google Scholar 

  25. Ochoa, G., Veerapen, N., Daolio, F., Tomassini, M.: Understanding phase transitions with local optima networks: number partitioning as a case study. In: Hu, B., López-Ibáñez, M. (eds.) Evolutionary Computation in Combinatorial Optimization, pp. 233–248. Springer International Publishing, Cham (2017)

    Chapter  Google Scholar 

  26. Ochoa, G., Verel, S., Daolio, F., Tomassini, M.: Local optima networks: a new model of combinatorial fitness landscapes. In: Richter, H., Engelbrecht, A. (eds.) Recent Advances in the Theory and Application of Fitness Landscapes, pp. 233–262. Springer, Berlin Heidelberg, Berlin, Heidelberg (2014)

    Chapter  Google Scholar 

  27. Öktem, H., Pearson, R., Egiazarian, K.: An adjustable aperiodic model class of genomic interactions using continuous time Boolean networks (Boolean delay equations). Chaos 13(4), 1167–1174 (2003)

    Article  MathSciNet  Google Scholar 

  28. Pitzer, E., Affenzeller, M.: A comprehensive survey on fitness landscape analysis. In: Fodor, J., Klempous, R., Araujo, S., Paz, C. (eds.) Recent Advances in Intelligent Engineering Systems, vol. 378, pp. 161–191. Springer, Berlin (2012)

    Chapter  Google Scholar 

  29. Stillinger, F.H., Weber, T.A.: Packing structures and transitions in liquids and solids. Science 225(4666), 983–989 (1984)

    Article  Google Scholar 

  30. Tokuda, I.T., Akman, O.E., Locke, J.C.: Reducing the complexity of mathematical models for the plant circadian clock by distributed delays. J. Theor. Biol. 463, 155–166 (2019)

    Article  MathSciNet  Google Scholar 

  31. Vérel, S., Daolio, F., Ochoa, G., Tomassini, M.: Local optima networks with escape edges. In: Hao, J.-K., Legrand, P., Collet, P., Monmarché, N., Lutton, E., Schoenauer, M. (eds.) Artificial Evolution, pp. 49–60. Springer, Berlin Heidelberg (2012)

    Chapter  Google Scholar 

  32. Verel, S., Ochoa, G., Tomassini, M.: Local optima networks of NK landscapes with neutrality. IEEE Trans. Evol. Comput. 15(6), 783–797 (2011)

    Article  Google Scholar 

  33. Wolfram, S.: Statistical mechanics of cellular automata. Rev. Mod. Phys. 55, 601–644 (1983)

    Article  MathSciNet  Google Scholar 

  34. Wright, S.: The roles of mutation, inbreeding, crossbreeding, and selection in evolution. In: Proceedings of 6th International Congress on Genetics, vol. 1, pp. 356–366 (1932)

    Google Scholar 

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Acknowledgements

This work was financially supported by the Engineering and Physical Sciences Research Council [grant number EP/N017846/1]. We would like to acknowledge the use of the University of Exeter High-Performance Computing (HPC) facility in carrying out this work. The authors would like to thank Sébastien Vérel and Gabriela Ochoa for providing inspirational invited talks on LONs at their institution during this grant.

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Authors and Affiliations

  1. Computer Science, University of Exeter, North Park Road, EX4 4QF, Exeter, UK

    Khulood Alyahya, Kevin Doherty, Ozgur E. Akman & Jonathan E. Fieldsend

  2. King Saud University, Riyadh, 11451, Saudi Arabia

    Khulood Alyahya

Authors
  1. Khulood Alyahya
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  2. Kevin Doherty
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  3. Ozgur E. Akman
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  4. Jonathan E. Fieldsend
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Corresponding author

Correspondence to Khulood Alyahya .

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Editors and Affiliations

  1. LIACS, Universiteit Leiden, Leiden, The Netherlands

    Mike Preuss

  2. The Signal Group, Athens, Greece

    Michael G. Epitropakis

  3. Computer Science and Software Engineering, RMIT University, Melbourne, VIC, Australia

    Xiaodong Li

  4. Department of Computer Science, University of Exeter, Exeter, UK

    Jonathan E. Fieldsend

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Alyahya, K., Doherty, K., Akman, O.E., Fieldsend, J.E. (2021). Reduced Models of Gene Regulatory Networks: Visualising Multi-modal Landscapes. In: Preuss, M., Epitropakis, M.G., Li, X., Fieldsend, J.E. (eds) Metaheuristics for Finding Multiple Solutions. Natural Computing Series. Springer, Cham. https://doi.org/10.1007/978-3-030-79553-5_10

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  • DOI: https://doi.org/10.1007/978-3-030-79553-5_10

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  • Online ISBN: 978-3-030-79553-5

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