Abstract
Mathematical modeling has become an integral part of synthesizing gene regulatory networks. One of the common problems is the determination of parameters, which are a part of the model description. In the present work, we propose a customized genetic algorithm as a method to determine the parameters such that the underlying oscillatory system exhibits the target behavior. We propose a problem specific, adaptive fitness function evaluation and a method to quantify the effect of a single parameter on the system response. The properties of the algorithm are highlighted and confirmed on two test cases of synthetic biological oscillators.
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References
Alon U (2007) An introduction to systems biology: design principles of biological circuits. Chapman & Hall/CRC, New York
Back T (1992) Self-adaptation in genetic algorithms. In: Towards a practice of autonomous systems proceedings of the first European conference on artificial life. MIT Press, Cambridge, pp 263–271
Butz M, Neuenschwander M, Kast P, Hilvert D (2011) An N-terminal protein degradation tag enables robust selection of highly active enzymes. Biochem Cell Biol 50(40):8594–8602
Chambers LD (2000) The practical handbook of genetic algorithms: applicationsations. Chapman and Hall/CRC, Perth
Dill KA, Fiebig KM, Chan HS (1993) Cooperativity in protein-folding kinetics. Proc Natl Acad Sci USA 90(5):1942–1946
Elowitz MB, Leibler S (2000) A synthetic oscillatory network of transcriptional regulators. Nat Biotechnol 403(6767):335–338
Fang F, Ni BJ, Yu HQ (2009) Estimating the kinetic parameters of activated sludge storage using weighted non-linear least-squares and accelerating genetic algorithm. Water Res 43(10):2595–2604
Farmani R, Wright J (2003) Self-adaptive fitness formulation for constrained optimization. IEEE Trans Evol Comput 7(5):445–455
François P, Hakim V (2004) Design of genetic networks with specified functions by evolution in silico. Proc Natl Acad Sci USA 101(2):580–585
Hajimorad M, Gray PR, Keasling JD (2011) A framework and model system to investigate linear system behavior in Escherichia coli. J Biol Eng 5(1):3
Law N, Szeto K (2007) Adaptive genetic algorithm with mutation and crossover matrices. In: Proceedings of the 20th international joint conference on artificial intelligence, Hyderabad, India, pp 2330–2333
Lillacci G, Khammash M (2010) Parameter estimation and model selection in computational biology. PLoS Comput Biol 6(3):696
Lillacci G, Khammash M (2012) A distribution matching method for parameter estimation and model selection in computational biology. Int J Robust Nonlinear Control 22:1065–1081
Mackey M, Glass L (1977) Oscillation and chaos in physiological control systems. Sci Agric 197(4300):287–289
Morton AJ, Wood NI, Hastings MH, Hurelbrink C, Barker Ra, Maywood ES (2005) Disintegration of the sleep-wake cycle and circadian timing in Huntington’s disease. J Neurosci 25(1):157–163
Novák B, Tyson JJ (2008) Design principles of biochemical oscillators. Nat Rev Mol Cell Biol 9(12):981–991
Paladugu S, Chickarmane V (2006) In silico evolution of functional modules in biochemical networks. Syst Biol 153(4):223–236
Rhodius VA, Mutalik VK, Gross CA (2012) Predicting the strength of UP-elements and full-length E. coli σE promoters. Nucl Acids Res 40(7):2907–2924
Rodrigo G, Jaramillo A (2012) AutoBioCAD: full biodesign automation of genetic circuits. ACS Synth Biol. doi:10.1021/sb300084h
Rodrigo G, Carrera J, Jaramillo A (2007) Genetdes: automatic design of transcriptional networks. Bioinformatics (Oxford, England) 23(14):1857–1858
Roy SW (2009) Probing evolutionary repeatability: neutral and double changes and the predictability of evolutionary adaptation. PloS One 4(2):e4500
Salis HM, Mirsky EA, Voigt CA (2009) Automated design of synthetic ribosome binding sites to control protein expression. Nature Biotechnol 27(10):946–950
Scheper T, Klinkenberg D, Pennartz C, van Pelt J (1999) A mathematical model for the intracellular circadian rhythm generator. J Neurosci 19(1):40–47
Smith J, Fogarty T (1996) Self adaptation of mutation rates in a steady state genetic algorithm. In: Proceedings of IEEE international conference on evolutionary computation, pp 318–323
Szendro IG, Franke J, de Visser JAGM, Krug J (2013) Predictability of evolution depends nonmonotonically on population size. Proc Natl Acad Sci USA 110(2):571–576
Tigges M, Marquez-Lago TT, Stelling J, Fussenegger M (2009) A tunable synthetic mammalian oscillator. Nature 457(7227):309–312. doi:10.1038/nature07616, URL http://www.ncbi.nlm.nih.gov/pubmed/19148099
Turek FW, Joshu C, Kohsaka A, Lin E, Ivanova G, McDearmon E, Laposky A, Losee-Olson S, Easton A, Jensen DR, Eckel RH, Takahashi JS, Bass J (2005) Obesity and metabolic syndrome in circadian Clock mutant mice. Science (New York, NY) 308(5724):1043–1045
Vecchi MP, Kirkpatrick S, Gelatt CD (1987) Optimization by simulated annealing, vol 220. Sci N Ser 220(4598):671–680
Weinreich DM, Chao L (2005) Rapid evolutionary escape by large populations from local fitness peaks is likely in nature. Evolution 59(6):1175–1182
Wu YH, Fischer DF, Kalsbeek A, Garidou-Boof ML, van der Vliet J, van Heijningen C, Liu RY, Zhou JN, Swaab DF (2006) Pineal clock gene oscillation is disturbed in Alzheimer’s disease, due to functional disconnection from the ”master clock”. FASEB J 20(11):1874–1876
Yokobayashi Y, Weiss R, Arnold FH (2002) Directed evolution of a genetic circuit. Proc Natl Acad Sci USA 99(26):16587–16591
Acknowledgements
The research was supported by the scientific research programme Pervasive Computing (P2-0359) financed by Slovenian Research Agency in years from 2009 to 2012. Results presented here are in scope of Ph.D. thesis that is being prepared by Martin Stražar.
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Stražar, M., Mraz, M., Zimic, N. et al. An adaptive genetic algorithm for parameter estimation of biological oscillator models to achieve target quantitative system response. Nat Comput 13, 119–127 (2014). https://doi.org/10.1007/s11047-013-9383-8
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DOI: https://doi.org/10.1007/s11047-013-9383-8