Fuzzy Logic in Genetic Regulatory Network Models

Authors

  • Carlos Muñoz Poblete University of La Frontera Avenue Francisco Salazar 01145, Temuco, Chile
  • Francisco Vargas Parra University of La Frontera Avenue Francisco Salazar 01145, Temuco, Chile
  • Jaime Bustos Gomez University of La Frontera Avenue Francisco Salazar 01145, Temuco, Chile
  • Millaray Curilem Saldias University of La Frontera Avenue Francisco Salazar 01145, Temuco, Chile
  • Sonia Salvo Garrido University of La Frontera Avenue Francisco Salazar 01145, Temuco, Chile
  • Horacio Miranda Vargas University of La Frontera Avenue Francisco Salazar 01145, Temuco, Chile

Keywords:

Genetic Regulatory Network, Fuzzy Logic, ANFIS, Differential Equations, Lac Operon

Abstract

Interactions between genes and the proteins they synthesize shape genetic regulatory networks (GRN). Several models have been proposed to describe these interactions, been the most commonly used those based on ordinary differential equations (ODEs). Some approximations using piecewise linear differential equations (PLDEs), have been proposed to simplify the model non linearities. However they not allways give good results. In this context, it has been developed a model capable of representing small GRN, combining characteristics from the ODE’s models and fuzzy inference systems (FIS). The FIS is trained through an artificial neural network, which forms an Adaptive Nertwork-based Fuzzy Inference System (ANFIS). This network allows to adapt the membership and output functions from the FIS according to the training data, thus, reducing the previous knowledge needed to model the specific phenomenon.
In addition, Fuzzy Logic allows to express their rules through linguistic labels, which also allows to incorporate expert knowledge in a friendly way. The proposed model has been used to describe the Lac Operon in E. Coli and it has been compared with the models already mentioned. The outcome errors due to the training process of the ANFIS network are comparable with those of the models based on ODEs. Additionally, the fuzzy logic approach provides modeling flexibility and knowledge acquisition advantages.

References

G. Acu-a, E. Cubillos, Development of a Matlab Toolbox for the Design of Grey-Box Neural Models, International Journal of Computers, Communications and Control, Vol. 1, pp. 7-14, 2006. http://dx.doi.org/10.15837/ijccc.2006.2.2280

D. Akçay, Inference Of Switching Networks By Using A Piecewise Linear Formulation, Institute of Applied Mathematics, METU, MSc thesis, 2005

F. A. Cubillos, G. Acu-a and E. L. Lima, Real-Time Process Optimization Based on Grey-Box Neural Models, Brazilian Journal of Chemical Engineering, Vol. 24, pp. 433-443, 2007. http://dx.doi.org/10.1590/S0104-66322007000300012

H. De Jong, Modeling and Simulation of Genetic Regulatory Systems: A Literature Review, Journal of Computacional Biology, Vol. 9, pp. 67-1003, 2002. http://dx.doi.org/10.1089/10665270252833208

N. Friedman, M. Linial, I. Nachman, and D. Pe'er, Using Bayesian Networks to Analyze Expression Data, Journal of Computational Biology, Vol. 7, pp. 601-620, 2000. http://dx.doi.org/10.1089/106652700750050961

J. Gebert, N. Radde, and G.Weber, Modeling gene regulatory networks with piecewise linear differential equations, European Journal of Operational Research, in press, 2006.

B. C. Goodwin, Oscillatory behaviour in enzymatic control process, Adv. Enz. Regul. Vol. 3, pp. 425-438, 1969. http://dx.doi.org/10.1016/0065-2571(65)90067-1

A. Halász, V. Kumar, M. Imielinski, C. Belta, O. Sokolsky, S. Pathak, and H. Rubin, Analysis of lactose metabolism in E.coli using reachability analysis of hybrid systems, IET Systems Biology, Vol. 1, pp. 130-148, 2007. http://dx.doi.org/10.1049/iet-syb:20060035

S. Kim, J. Kim, and C. Kwang-Hyun, Inferring gene regulatory networks from temporal expression profiles under time-delay and noise, Computational Biology and Chemistry, Vol. 31, pp. 239-245, 2007. http://dx.doi.org/10.1016/j.compbiolchem.2007.03.013

W. A. Knorre, Oscillation of the rate of synthesis of b -galactosidase in Escherichia Coli ML 30 and ML 308, Biochem. Biophys. Res. Commun, Vol. 31, pp. 812-817, 1968. http://dx.doi.org/10.1016/0006-291X(68)90635-9

A. Kremling, K. Bettenbrock, B. Laube, K. Jahreis, W. Lengeler, and E. Gilles, The Organization of Metabolic Reaction Networks III. Application for Diauxic Growth on Glucose and Lactose, Metabolic Engineering, Vol 3, pp. 362-379, 2001. http://dx.doi.org/10.1006/mben.2001.0199

R. Linden, and A. Bhaya, Evolving fuzzy rules to model gene expression, BioSystems, Vol. 88, pp. 76-91, 2007. http://dx.doi.org/10.1016/j.biosystems.2006.04.006

B. Lee, J. Yen, L. Yang, and J. Liao, Incorporating Qualitative Knowledge in enzyme kinetic Models Using Fuzzy Logic, Biotechnology and Bioengineering, Vol. 62, pp. 722-729, 1999. http://dx.doi.org/10.1002/(SICI)1097-0290(19990320)62:63.0.CO;2-U

H. McAdams, and L. Shapiro, Circuit Simulation of Genetic Networks, Science, Vol. 269, pp. 650-656, 1995. http://dx.doi.org/10.1126/science.7624793

S. Pestka, B. L. Daugherty, V. Jung, K. Hotta, and R. K. Pestka, Anti-mRNA: specific inihbition of translation of single mRNA molecules, Proc. Natl. Acad. Sci. USA, Vol. 81, pp. 7525-7528, 1984. http://dx.doi.org/10.1073/pnas.81.23.7525

H. Ressom, P. Natarajan, R. S. Varghese, and M. T. Musavi, Applications of fuzzy logic in genomics, Fuzzy Sets and Systems, Vol. 152, pp. 125-138, 2005. http://dx.doi.org/10.1016/j.fss.2004.10.018

J. Shing, and R. Jang, ANFIS: Adaptive-Network-Based Fuzzy Inference System, Trans. on Systems, Man and Cybernetics, Vol. 23, pp. 665-685, 1993. http://dx.doi.org/10.1109/21.256541

P. Smolen, D. Baxter, and J. Byrne, Modeling Transcriptional Control in Gene Networks - Methods, Recents Results, and Future Directions, Bulletin of Mathematical Biology, Vol. 62, pp. 247-292, 2000. http://dx.doi.org/10.1006/bulm.1999.0155

B. A. Sokhansanj, and J. P. Fitch, URC Fuzzy Modeling and Simulation of Gene Regulation, 23rd Annual Internacional Conference of the IEEE Engineering in Medicine and Biology, Instanbul, Turkey, 2001.

A. Tepeli, and A. Hortaçsu, A fuzzy logic approach for regulation in flux balance analysis, Biochemical Engineering Journal, in press, 2007.

F. Vargas, C. Mu-oz, and J. Bustos, Fuzzy Logic in Gene Regulatory Networks Models, 1st Internacional CGNA Workshop, Utilizacion Of Novel And Sustainable Plant Products In Aqua-Feeds, Temuco, Chile, 2008.

S. Vinterbo, E. Y. Kim, and L. Ohno-Machado, Small, fuzzy and interpretable gene expression based classifiers, Bioinformatics, Vol. 21, pp. 1964-1970, 2005. http://dx.doi.org/10.1093/bioinformatics/bti287

P. Wong, S. Gladney, and J. Keasling, Mathematical Model of the lac Operon: Inducer Exclusion, Catabolite Repression, and Diauxic Growth on Glucose and Lactose, Biotechnol. Prog, Vol. 13, pp. 132-143, 1997. http://dx.doi.org/10.1021/bp970003o

P. Woolf, and Y. Wang, A fuzzy logic approach to analyzing gene expression data, Physiol Genomics, Vol. 3, pp. 9-15, 2000.

N. Yildirim, and M. Mackey, Feedback Regulation in the Lactose Operon: A Matematical Modeling Study and Comparison with Experimental Data, Biophysical Journal, Vol. 84, pp. 2841-2851, 2003. http://dx.doi.org/10.1016/S0006-3495(03)70013-7

X. Zhu, and J. Xu, Estimation of time varying parameters in nonlinear systems by using dynamic optimization, Industrial Electronics Society. IECON 2005. 31st Annual Conference of IEEE, 2005.

Published

2009-12-01

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