Buradasınız

Anasayfa » Content

Estimating Stable Uncertainty Sets for Genetic Regulatory Networks with Guaranteed Disturbance Attenuation

Journal Name:

  • Journal of Control Engineering and Technology

Publication Year:

  • 2014

Keywords (Original Language):

Author NameUniversity of Author
Bookmark/Search this post with
Abstract (Original Language): 
It is well-known that models of genetic regulatory networks (GRNs) are unavoidably affected by uncertainties. This paper addresses the problem of estimating stable uncertainty sets of uncertain GRNs with guaranteed disturbance attenuation. Specifically, the GRNs are assumed to be affected by disturbances in the form of Wiener processes, and by uncertainties in the form of a parameter vector that determines the coefficients of the model via given functions. It is shown that estimates of the sought stable uncertainty sets can be obtained through a recursive strategy based on parameter-dependent Lyapunov functions and convex optimization. Some examples with fictitious and real biological models illustrate the use of the proposed strategy.
FULL TEXT (PDF): 
PDF icon arastirmax-estimating-stable-uncertainty-sets-genetic-regulatory-networks-guaranteed-disturbance-attenuation.pdf
  • 1
22
28
  • English

REFERENCES

References: 

H. De Jong, “Modelling and simulation of genetic regulatory systems: A literature review”, Journal of computational biology, vol. 9, no. 1, pp. 67-103, 2002.
O. Wolkenhauer and M. Mesarovic, “Feedback dynamics and cell function: Why systems biology is called Systems Biology”, MolecularBioSystems, vol. 1, no. 1, pp. 14-16, 2005.
G. Chesi, “Polynomial relaxation-based conditions for global asymptotic stability of equilibrium points of genetic regulatory networks”, Int. Journal of Systems Science, vol. 41, no. 1, pp. 65-72, 2010.
L. Chen, R. Wang and X. Zhang, Biomolecular Networks: Methods And Applications In Systems Biology, Wiley Series In Bioinformatics, 2009.
P. Li and J. Lam, “Disturbance analysis of nonlinear differential equation models of genetic SUM regulatory networks”, IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 8, pp.253-259, 2011.
P. Smolen, D. A. Baxter and J. H. Byrne, “Mathematical modeling of gene networks”, Neuron, vol. 26, no. 3, pp. 567-580, 2000.
H. Bolouri and E. H. Davidson, “Modelling transcriptional regulatory networks”, BioEssay, vol. 24, pp. 1118-1129, 2002.
J. Aracena, S. B. Lamine, M. A. Mermet, O. Cohen and J. Demongeot, “Mathematical modeling in genetic networks: Relationships between the genetic expression and both chromosomic breakage and positive circuits”, IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, vol. 33, no. 5, pp. 825-834, 2003.
C. J. Tomlin and J. D. Axelrod, “Biology by numbers: mathematical modelling in developmental biology”, Nature Reviews Genetics, vol. 8, pp. 331-340, 2007.
T. Schlitt and A. Brazma, “Current approaches to gene regulatory network modelling”, BMC Bioinformatics, vol.8, no. Suppl.6, pp. S9, 2007.
G. Chesi, “Robustness analysis of genetic regulatory networks affected by model uncertainty”, Automatica, vol. 47, no. 6, pp. 1131-1138, 2011.
C. Li, L. Chen and K. Aihara, “Stability of genetic networks wirh SUM regulatory logic: Lur'e system and LMI approach”, IEEE Trans. On circuits and systems I, vol. 53, no. 11, pp. 2451-2458, 2006.
W. Pan, Z. Wang, H. Gao and X. Liu, “Monostability and multistability of genetic regulatory networks with different types of regulation functions”, Nonlinear Analysis: Real World Applications, vol. 11, no. 4, pp. 3170-3185, 2010.
I. Shmulevich, E. R. Dougherty and W. Zhang, “From Boolean to probabilistic Boolean networks as models of genetic regulatory networks”, Proceedings of the IEEE, vol. 90, no. 11, pp. 1778-1792, 2002.
J. M. Bower and H. Bolouri, Computational modeling of genetic and biochemical networks, MIT Press, Cambridge, 2001.
P. Li, J. Lam and Z. Shu, “On the transient and steady-state estimates of interval genetic regulatory networks”, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 40, no. 2, pp. 336-349, 2010.
J. M. Raser and E. K. O'Shea, “Noise in gene expression: Origins, consequences, and control”, Science, vol. 309, pp. 2010-2013 ,2005.
G. Chesi, “On the Steady States of Uncertain Genetic Regulatory Networks," IEEE Transactions on Systems, Man and Cybernetics - Part A, vol. 42, no. 4, pp. 1020-1024, 2012.
P. Balasubramaniam, R. Rakkiyappan and R. Krishnasamy, “Stochastic stability of Markovian jumping uncertain stochastic genetic regulatory networks with interval time-varying delays”, Mathematical Biosciences, vol. 226, no. 2, pp. 97-108, 2010.
Journal of Control Engineering and Technology (JCET)
JCET Vol. 4 Iss. 1 January 2014 PP. 22-28 www.ijcet.org © American V-King Scientific Publish
28
D. Bratsun, D. Volfson, L. S. Tsimring and J. Hasty, “Delay-induced stochastic oscillations in gene regulation”, Proceedings of the National Academy of Sciences of the United States of America, vol. 102, no. 41, pp. 14593-14598, 2005. M. B. Elowitz, A. J. Levine, E. D. Siggia and P. S. Swain, “Stochastic gene expression in a single cell”, Science, vol. 297, pp. 1183-1186, 2002. S. Aluru, Handbook of computational molecular biology, Chapman and ALL/Crc Computer and Information Science Series, Oxford, UK, 2005.
L. Chen and K. Aihara, “Stability of genetic regulatory networks with time delay”, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 49, no. 5, pp. 602-608, 2002. G. Chesi, “Computing equilibrium points of genetic regulatory networks”, Trans. on Computational Systems Biology, vol. 5750, pp. 268-282, 2009. P. Dhaeseleer, S. Liang and R. Somogyi, “Genetic network inference: from co-expression clustering to reverse engineering”, Bioinformatics, vol. 16, no. 8, pp. 707-726, 2000. G. Chesi and Y. S. Hung, “Stability analysis of uncertain genetic SUM regulatory networks”, Automatica, vol. 44, no. 9, pp. 2298-2305, 2008. C. Li, L. Chen and K. Aihara, “Stochastic stability of genetic networks with disturbance attenuation”, IEEE Trans. on circuits and systems II, vol. 54, no. 10, pp. 892-896, 2007. N. E. Buchler, U. Gerland and T. Hwa, “On schemes of combinatorial transcription logic”, Proceedings of the National Academy of Sciences, vol. 100, pp. 5136-5141, 2003. G. Chesi, “LMI techniques for optmization over polynomials in control: a survey”, IEEE Trans. on Automatic Control, vol. 55, no. 11, pp. 2500-2510, 2010. M. B. Elowitz and S. Leibler, “A synthetic oscillatory network of transcriptional regulators”, Nature, vol. 403, pp. 335-338, 2000.

Thank you for copying data from http://www.arastirmax.com