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2016, 13(6): 1207-1222. doi: 10.3934/mbe.2016039

Sensitivity of signaling pathway dynamics to plasmid transfection and its consequences

Jaroslaw Smieja 1, and  Marzena Dolbniak 2,

1. 

Institute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-101 Gliwice
2. 

Institute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland

Received  October 2015 Revised  March 2016 Published  August 2016

This paper deals with development of signaling pathways models and using plasmid-based experiments to support parameter estimation. We show that if cells transfected with plasmids are used in experiments, the models should include additional components that describe explicitly effects induced by plasmids. Otherwise, when the model is used to analyze responses of wild type, i.e. non-transfected cells, it may not capture their dynamics properly or even lead to false conclusions. In order to illustrate this, an original mathematical model of miRNA-mediated control of gene expression in the NF$\kappa$B pathway is presented. The paper shows what artifacts might appear due to experimental procedures and how to develop the models in order to avoid pursuing these artifacts instead of real kinetics.
Keywords: sensitivity., plasmid transfection, Signaling pathways modeling.
Mathematics Subject Classification: Primary: 92C42; Secondary: 92C3.
Citation: Jaroslaw Smieja, Marzena Dolbniak. Sensitivity of signaling pathway dynamics to plasmid transfection and its consequences. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1207-1222. doi: 10.3934/mbe.2016039
References:
[1]

S. T. M. Allard and K. Kopish, Luciferase reporter assays: Powerful, adaptable tools for cell biology research, Cell Notes, 21 (2008), 23-26. Google Scholar

[2]

J. Bachmann, A. Raue, M. Schilling, V. Becker, J. Timmer and U. Klingmueller, Predictive mathematical models of cancer signalling pathways, J. Intern. Med., 271 (2012), 155-165. doi: 10.1111/j.1365-2796.2011.02492.x.  Google Scholar

[3]

D. Bakstad, A. Adamson, D. G. Spiller and M. R. White, Quantitative measurement of single cell dynamics, Curr. Opin. Biotechnol., 23 (2013), 103-109. doi: 10.1016/j.copbio.2011.11.007.  Google Scholar

[4]

S. Basak, M. Behar and A. Hoffmann, Lessons from mathematically modeling the NF-$\kappa$B pathway, Immunol. Rev., 1 (2012), 221-238. Google Scholar

[5]

I. Bentwich, A. Avniel, Y. Karov, R. Aharonov, S. Gilad, O. Barad, A. Barzilai, P. Einat, U. Einav, E. Meiri, E. Sharon, Y. Spector and Z. Bentwich, Identification of hundreds of conserved and nonconserved human microRNAs, Nat. Genet., 37 (2005), 766-770. doi: 10.1038/ng1590.  Google Scholar

[6]

R. Cheong, A. Bergmann, S. L. Werner, J. Regal and A. Hoffmann, Transient I$\kappa$B kinase activity mediates temporal NF-$\kappa$B dynamics in response to wide range of tumour necrosis factor-$\alpha$ doses, J. Biol. Chem., 281 (2006), 2945-2950. Google Scholar

[7]

A. E. Erson-Bensan, Introduction to microRNAs in biological systems, Methods Mol. Biol., 1107 (2014), 1-14. doi: 10.1007/978-1-62703-748-8_1.  Google Scholar

[8]

R. C. Friedman, K. K. Farh, C. B. Burge and D. P. Bartel, Most mammalian mRNAs are conserved targets of microRNAs, Genome Res., 19 (2009), 92-105. doi: 10.1101/gr.082701.108.  Google Scholar

[9]

A. Grimson, K. K. Farh, W. K. Johnston, P. Garrett-Engele, L. P. Lim and D. Bartel, MicroRNA Targeting Specificity in Mammals: Determinants beyond Seed Pairing, Mol. Cell, 27 (2007), 91-105. doi: 10.1016/j.molcel.2007.06.017.  Google Scholar

[10]

J. Hayes, P. P. Peruzzi and S. Lawler, MicroRNAs in cancer: Biomarkers, functions and therapy, Trends Mol. Med., 20 (2014), 460-469. doi: 10.1016/j.molmed.2014.06.005.  Google Scholar

[11]

P. Iglesias and B. Ingalls (editors), Control Theory and Systems Biology, MIT Press, Cambridge, Mass., 2010.  Google Scholar

[12]

B. P. Lewis, C. B. Burge and D. P. Bartel, Conserved seed pairing, often flanked by adenosines, indicates that thousands of human genes are microRNA targets, Cell, 120 (2005), 15-20. Google Scholar

[13]

L. P. Lim, N. C. Lau, E. G. Weinstein, A. Abdelhakim, S. Yekta, M. W. Rhoades, C. B. Burge and D. P. Bartel, The microRNAs of Caenorhabditis elegans, Genes Dev., 17 (2003), 991-1008. doi: 10.1101/gad.1074403.  Google Scholar

[14]

T. Lipniacki, P. Paszek, A. R. Brasier, B. Luxon and M. Kimmel, Mathematical model of NF$\kappa$B regulatory module, J. Theor. Biol., 228 (2004), 195-215. doi: 10.1016/j.jtbi.2004.01.001.  Google Scholar

[15]

J. Smieja, Coupled analytical and numerical approach to uncovering new regulatory mechanisms of intracellular processes, Int. J. Appl. Math. Comp. Sci., 20 (2010), 781-788. Google Scholar

[16]

J. Smieja and M. Dolbniak, Experimental data in modeling of intracellular processes, Proc. IASTED Int. Conf. Modelling, Identification and Control (MIC 2015), (2015), 105-109. doi: 10.2316/P.2015.826-016.  Google Scholar

[17]

Y. Takei, M. Takigahira, K. Mihara, Y. Tarumi and K. Yanagihara, The metastasis-associated microRNA miR-516a-3p is a novel therapeutic target for inhibiting peritoneal dissemination of human scirrhous gastric cancer, Cancer Res., 71 (2011), 1442-1453. doi: 10.1158/0008-5472.CAN-10-2530.  Google Scholar

[18]

D. A. Turner, P. Paszek, D. J. Woodcock, C. A. Horton, Y. Wang, D. G. Spiller, D. A. Rand, M. R. H. White and C. V. Harper, Physiological levels of TNF $\alpha$ stimulation induce stochastic dynamics of NF-$\kappa$B responses in single living cells, J. Cell Sci., 324 (2010), 2834-2843. Google Scholar

[19]

J. J. Tyson, R. Albert, A. Goldbeter, P. Ruoff and J. Sible, Biological switches and clocks, J. R. Soc. Interface, 5 (2008), S1-S8. doi: 10.1098/rsif.2008.0179.focus.  Google Scholar

[20]

A. V. Orang, R. Safaralizadeh and M. Kazemzadeh-Bavili, Mechanisms of miRNA-Mediated Gene Regulation from Common Downregulation to mRNA-Specific Upregulation. Int. J. Genomics, 2014 (2014), 970607. Google Scholar

[21]

X. Wang, Y. Li, X. Xu and Y. H. Wang, Toward a system-level understanding of microRNA pathway via mathematical modeling, Biosystems, 100 (2010), 31-38. doi: 10.1016/j.biosystems.2009.12.005.  Google Scholar

[22]

R. A. Williams, J. Timmis and E. E. Qwarnstrom, Computational models of the NF-$\kappa$B signalling pathway, Computation, 2 (2014), 131-158. Google Scholar

[23]

X. Xue, W. Xia and H. Wenzhong, A modeled dynamic regulatory network of NF-kB and IL-6 mediated by miRNA, BioSystems, 114 (2013), 214-218. Google Scholar

[24]

F. Yan, H. Liu and Z. Liu, Dynamic analysis of the combinatorial regulation involving transcription factors and microRNAs in cell fate decisions, Bioch et Biophysica Acta, 1844 (2014), 248-257. doi: 10.1016/j.bbapap.2013.06.022.  Google Scholar

[25]

W. Zhou, Y. Li, X. Wang, L. Wu and Y. Wang, MiR-206-mediated dynamic mech-anism of the mammalian circadian clock, BMC Syst. Biol., 5 (2011), 141. Google Scholar

show all references

References:
[1]

S. T. M. Allard and K. Kopish, Luciferase reporter assays: Powerful, adaptable tools for cell biology research, Cell Notes, 21 (2008), 23-26. Google Scholar

[2]

J. Bachmann, A. Raue, M. Schilling, V. Becker, J. Timmer and U. Klingmueller, Predictive mathematical models of cancer signalling pathways, J. Intern. Med., 271 (2012), 155-165. doi: 10.1111/j.1365-2796.2011.02492.x.  Google Scholar

[3]

D. Bakstad, A. Adamson, D. G. Spiller and M. R. White, Quantitative measurement of single cell dynamics, Curr. Opin. Biotechnol., 23 (2013), 103-109. doi: 10.1016/j.copbio.2011.11.007.  Google Scholar

[4]

S. Basak, M. Behar and A. Hoffmann, Lessons from mathematically modeling the NF-$\kappa$B pathway, Immunol. Rev., 1 (2012), 221-238. Google Scholar

[5]

I. Bentwich, A. Avniel, Y. Karov, R. Aharonov, S. Gilad, O. Barad, A. Barzilai, P. Einat, U. Einav, E. Meiri, E. Sharon, Y. Spector and Z. Bentwich, Identification of hundreds of conserved and nonconserved human microRNAs, Nat. Genet., 37 (2005), 766-770. doi: 10.1038/ng1590.  Google Scholar

[6]

R. Cheong, A. Bergmann, S. L. Werner, J. Regal and A. Hoffmann, Transient I$\kappa$B kinase activity mediates temporal NF-$\kappa$B dynamics in response to wide range of tumour necrosis factor-$\alpha$ doses, J. Biol. Chem., 281 (2006), 2945-2950. Google Scholar

[7]

A. E. Erson-Bensan, Introduction to microRNAs in biological systems, Methods Mol. Biol., 1107 (2014), 1-14. doi: 10.1007/978-1-62703-748-8_1.  Google Scholar

[8]

R. C. Friedman, K. K. Farh, C. B. Burge and D. P. Bartel, Most mammalian mRNAs are conserved targets of microRNAs, Genome Res., 19 (2009), 92-105. doi: 10.1101/gr.082701.108.  Google Scholar

[9]

A. Grimson, K. K. Farh, W. K. Johnston, P. Garrett-Engele, L. P. Lim and D. Bartel, MicroRNA Targeting Specificity in Mammals: Determinants beyond Seed Pairing, Mol. Cell, 27 (2007), 91-105. doi: 10.1016/j.molcel.2007.06.017.  Google Scholar

[10]

J. Hayes, P. P. Peruzzi and S. Lawler, MicroRNAs in cancer: Biomarkers, functions and therapy, Trends Mol. Med., 20 (2014), 460-469. doi: 10.1016/j.molmed.2014.06.005.  Google Scholar

[11]

P. Iglesias and B. Ingalls (editors), Control Theory and Systems Biology, MIT Press, Cambridge, Mass., 2010.  Google Scholar

[12]

B. P. Lewis, C. B. Burge and D. P. Bartel, Conserved seed pairing, often flanked by adenosines, indicates that thousands of human genes are microRNA targets, Cell, 120 (2005), 15-20. Google Scholar

[13]

L. P. Lim, N. C. Lau, E. G. Weinstein, A. Abdelhakim, S. Yekta, M. W. Rhoades, C. B. Burge and D. P. Bartel, The microRNAs of Caenorhabditis elegans, Genes Dev., 17 (2003), 991-1008. doi: 10.1101/gad.1074403.  Google Scholar

[14]

T. Lipniacki, P. Paszek, A. R. Brasier, B. Luxon and M. Kimmel, Mathematical model of NF$\kappa$B regulatory module, J. Theor. Biol., 228 (2004), 195-215. doi: 10.1016/j.jtbi.2004.01.001.  Google Scholar

[15]

J. Smieja, Coupled analytical and numerical approach to uncovering new regulatory mechanisms of intracellular processes, Int. J. Appl. Math. Comp. Sci., 20 (2010), 781-788. Google Scholar

[16]

J. Smieja and M. Dolbniak, Experimental data in modeling of intracellular processes, Proc. IASTED Int. Conf. Modelling, Identification and Control (MIC 2015), (2015), 105-109. doi: 10.2316/P.2015.826-016.  Google Scholar

[17]

Y. Takei, M. Takigahira, K. Mihara, Y. Tarumi and K. Yanagihara, The metastasis-associated microRNA miR-516a-3p is a novel therapeutic target for inhibiting peritoneal dissemination of human scirrhous gastric cancer, Cancer Res., 71 (2011), 1442-1453. doi: 10.1158/0008-5472.CAN-10-2530.  Google Scholar

[18]

D. A. Turner, P. Paszek, D. J. Woodcock, C. A. Horton, Y. Wang, D. G. Spiller, D. A. Rand, M. R. H. White and C. V. Harper, Physiological levels of TNF $\alpha$ stimulation induce stochastic dynamics of NF-$\kappa$B responses in single living cells, J. Cell Sci., 324 (2010), 2834-2843. Google Scholar

[19]

J. J. Tyson, R. Albert, A. Goldbeter, P. Ruoff and J. Sible, Biological switches and clocks, J. R. Soc. Interface, 5 (2008), S1-S8. doi: 10.1098/rsif.2008.0179.focus.  Google Scholar

[20]

A. V. Orang, R. Safaralizadeh and M. Kazemzadeh-Bavili, Mechanisms of miRNA-Mediated Gene Regulation from Common Downregulation to mRNA-Specific Upregulation. Int. J. Genomics, 2014 (2014), 970607. Google Scholar

[21]

X. Wang, Y. Li, X. Xu and Y. H. Wang, Toward a system-level understanding of microRNA pathway via mathematical modeling, Biosystems, 100 (2010), 31-38. doi: 10.1016/j.biosystems.2009.12.005.  Google Scholar

[22]

R. A. Williams, J. Timmis and E. E. Qwarnstrom, Computational models of the NF-$\kappa$B signalling pathway, Computation, 2 (2014), 131-158. Google Scholar

[23]

X. Xue, W. Xia and H. Wenzhong, A modeled dynamic regulatory network of NF-kB and IL-6 mediated by miRNA, BioSystems, 114 (2013), 214-218. Google Scholar

[24]

F. Yan, H. Liu and Z. Liu, Dynamic analysis of the combinatorial regulation involving transcription factors and microRNAs in cell fate decisions, Bioch et Biophysica Acta, 1844 (2014), 248-257. doi: 10.1016/j.bbapap.2013.06.022.  Google Scholar

[25]

W. Zhou, Y. Li, X. Wang, L. Wu and Y. Wang, MiR-206-mediated dynamic mech-anism of the mammalian circadian clock, BMC Syst. Biol., 5 (2011), 141. Google Scholar

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