Control Systems and Computers, N3, 2017, Article 7


Upr. sist. maš., 2017, Issue 3 (269), pp. 63-72.

UDC 574:004.9

Fefelov A.A., PhD in Techn. Sciences, Associate Professor, Department of Design,


Lytvynenko V.I., Doctor of Technical Sciences, Professor, Head of the Department of Informatics and Computer Science, E-mail:

Taif M.A., Graduate student of the Department of Informatics and Computer Science, E-mail:

Lurie I.A., PhD in Techn. Sciences, Associate Professor, E-mail:,

Kherson National Technical University, Bereslavskoe Shosse, 24, Kherson, 73008, Ukraine

Hybrid Approach for Gene Regulatory Networks Reconstruction by a System of Ordinary Differential Equations

Introduction. Although there are a variety of models and methods for gene regulatory networks reconstruction, the problem of obtaining an adequate model based on experimental data is still urgent. In this regard, many studies use a fixed record of the differential equations based on the S-system. A significant disadvantage of such fixed record of the differential equations is the lack of flexibility of the model, what limits the scope of its application.

Purpose. The purpose of this work is development of the hybrid procedure of the solution of the gene networks reconstruction problem based on the ordinary differential equations.

Method. Models of the ordinary differential equations are used to model the gene regulatory networks. To solve the differential equations, wavelet-neural networks are used. The topology and tuning of the parameters is determined using the algorithm of the clonal selection. To find the concentration of gene expression products, which are represented by the method of solving the Cauchy problem, the Runge-Kutta method of the fourth order is applied.

Results. A hybrid method is developed that implemented the procedure for reconstructing gene regulatory networks based on the gene expression data. The effectiveness of the proposed method is proved by experimental studies that confirm the applicability of this approach to find the relationships between the components of the GRN.

Conclusion. The proposed work is a new Wavelet Neural Network and Clonal Algorithm approach for inferring Gene Regulatory Network which is expressed in terms of the ordinary differential model. The result of the proposed procedure is that further improvement of the technology, combined with preprocessing methods, will allow the effective reconstruction of real GRN. The main directions of further research we have chosen to create a meta-procedure for automatic configuration of parameters of a hybrid algorithm. This meta-procedure will reduce the search space by dynamically changing the intervals of representation of the elements values that make up the individuals of the AIS. Using this new method the bioinformatics and biologists can infer any Gene Regulatory Network of their interest. Also, they can understand the regulatory mechanism of the specific genes which causes the combat diseases.

Keywords: gene regulatory networks, reverse engineering, gene expression, ordinary differential equations, clonal selection algorithm, wavelet-neural network.

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  1. Rawool, S.B., Venkatesh, K.V., 2007. “Steady state approach to model gene regulatory networks – simulation of microarray experiments”. Biosystems, 90(3), pp. 636–655.
  2. Chen, P.C.Y., Chen, J.W., 2007. “A Markovian approach to the control of genetic regulatory networks”. Biosystems, 90(2), pp. 535–545.
  3. DeRisi, J.L., Lyer, V.R, Brown, P.O., 1997. “Exploring the metabolic and genetic control of gene expression on a genomic scale”. Science, 278, pp. 680–686.
  4. Yaghoobi, H., Haghipour, S., Hamzeiy, H. et al., 2012. “A review of modeling techniques for genetic regulatory networks”. J. Med. Sign. Sens, 2 (1), pp. 61–70.
  5. Liang, S., Fuhrman, S., Somogyi, R., 1998. “Reveal, a general reverse engineering algorithm for inference of genetic network architectures”. Pacific Symp. on Biocomputing (PSB ’98), Jan. 1998: Proc., Maui, Hawaii, USA, pp. 18–29.
  6. Friedman, N., Linial, M., Nachman, I. et al., 2000. “Using Bayesian networks to analyze expression data”. J. of Computational Biology, 7(3–4), pp. 601–620.
  7. Chen, T., He, H.L., Church, G.M., 1999. “Modeling gene expression with differential equations”. 4th Pacific Symp. on Biocomputing (PSB ’99), Jan. 1999: Proc., Big Island of Hawaii, USA, pp. 29–40.
  8. Savageau, M.A., 1988. “Introduction to S-systems and the underlying power-law formalism”. Mathematical and Computer Modelling, 11, pp. 546–551.
  9. Dasgupta, D., 1999. “Artificial Immune Systems and Their Applications”. Springer-Verlag, 306 p.
  10. De Castro, L.N., Timmis, J., 2002. Artificial Immune Systems: A New Computational Intelligence Approach, Sprin¬ger, Heidelberg, 357 p.
  11. De Castro, L.N., Von Zuben, F.J., 1999. Artificial Immune Systems: Part I – Basic Theory and Applications, (Technical Report – RT DCA 01/99, FEEC/UNICAMP), Brazil, 95 p.
  12. De Castro, L.N., Von Zuben, F.J., 2000. Artificial Immune Systems: Part II – A Survey of Applications, (Technical Report – RT DCA 02/00, FEEC/UNICAMP), Brazil, 64 p.
  13. Bidyuk, P.I., Litvinenko, V.I., Fefelov, A.O., 2007. “Formalization of methods for constructing artificial immune systems”. Science news nats tech Unitary Enterprise of Ukraine “KPI”, 1, pp. 29-41.
  14. Galvao, R.K.H., Becerra, V.M., Calado, J.M.F. et al., 2004. “Linear-Wavelet Networks”. J. of Appl. Math. Comput. Sci., 14 (2), pp. 221–232.
  15. Oussar, Y., Dreyfus, G., 2000. “Initialization by Selection for Wavelet Network Training”. Neurocomputing, 34, pp. 131–143.
  16. Y. Oussar, I.Rivals, L. Personnaz et al., 1998. “Training Wavelet Networks for Nonlinear Dynamic Input-Output Modeling”. Neurocomputing, 20, pp. 173–188.
  17. Fefelov, A.A., Goravsky, S.P., Litvinenko, V.I., 2005. “Build and configure the veyvel-neural networks using artificial immune systems”. Sb. sciences works: 5 Intern. sciences conf. “Intellectual Systems of Decision-making and Problem of Computational Intelligence”, Evpatoria, T 5, pp. 77-80.
  18. Goldberg, D.E., Deb, K., 2014. “A comparative analysis of selection schemes used in genetic algorithms”. Foundations of genetic algorithms, Morgan Kaufmann, 341 p.
  19. Sakamoto, E., Iba, H., 2001. “Inferring a system of differential equations for a gene regulatory network by using genetic programming”. Congress on Evolutionary Computation, 27–30 May 2001: Proc., COEX, Seoul, Korea, pp. 720–726.
  20. Lekutai, G., 1997. Adaptive self-tuning neuro wavelet network controllers: thesis… PhD. The Electrical Engineering Department. Blacksburg, Virginia, 112 p.
  21. Weaver, D.C., Workman, C.T., Stormo, G.D., 1999. “Modeling regulatory networks with weight matrices”. Pacific Symp. on Biocomputing 4 (PSB ’99), 4–9 Jan. 1999: Proc., Maui, Hawaii, USA, pp. 112–123.

Received 07.03.2017