Experimental data for solid tumor cells: Proliferation curves and time-changes of heat shock proteins

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February 2012, 5(1): 235-244. doi: 10.3934/dcdss.2012.5.235

Experimental data for solid tumor cells: Proliferation curves and time-changes of heat shock proteins

Kazuhiko Yamamoto ^1, , Kiyoshi Hosono ^1, , Hiroko Nakayama ^1, , Akio Ito ^2, and Yuichi Yanagi ^3,

1.	Cluster of Biotechnology and Chemistry Systems, Graduate School of Systems Engineering, Kinki University, 1 Takayaumenobe, Higashihiroshima, Hiroshima, 739-2116, Japan, Japan, Japan
2.	Center for the Advancement of Higher Education, Faculty of Engineering, Kinki University, 1 Takayaumenobe, Higashihiroshima, Hiroshima, 739-2116, Japan
3.	Cluster of Electronic Engineering and Information Science, Graduate School of Systems Engineering, Kinki University, 1 Takayaumenobe, Higashihiroshima, Hiroshima, 739-2116, Japan

Received July 2009 Revised December 2009 Published February 2011

Abstract
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We consider a relation between proliferation of solid tumor cells and time-changes of the quantities of heat shock proteins in them. To do so, in the present paper we start to obtain some experimental data of the proliferation curves of solid tumor cells, actually, A549 and HepG2, as well as the time-changes of proteins, especially HSP90 and HSP72, in them. And we propose a mathematical model to re-create the experimental data of the proliferation curves and the time-changes of the quantities of heat shock proteins, which is described by ODE systems. Finally, we discuss a problem which exists between mitosis of solid tumor cells and time-changes of the quantities of heat shock proteins, from the viewpoint of biotechnology.

Keywords: Time-change of HSP., Experimental data, Proliferation curve.

Mathematics Subject Classification: Primary: 92C10, 92C99; Secondary: 92C4.

Citation: Kazuhiko Yamamoto, Kiyoshi Hosono, Hiroko Nakayama, Akio Ito, Yuichi Yanagi. Experimental data for solid tumor cells: Proliferation curves and time-changes of heat shock proteins. Discrete and Continuous Dynamical Systems - S, 2012, 5 (1) : 235-244. doi: 10.3934/dcdss.2012.5.235

References:

[1]	A. Ito, K. Yamamoto, Y. Yanagi and K. Hosono, Key-pathway analysis in biochemical reaction of HSP synthesis process, Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, Okayama, Japan, March 26-29, (2009), 474-479. doi: 10.1109/ICNSC.2009.4919322.
[2]	T. R. Rieger, R. I. Morimoto and V. Hatzimanikatis, Mathematical modeling of the eukaryotic heat-shock response: Dynamics of the HSP70 promoter, Biophysical Journal, 88 (2005), 1646-1658. doi: 10.1529/biophysj.104.055301.
[3]	Y. Yanagi and A. Ito, Numerical simulations of heat shock protein synthesis and tumor invasion phenimenon, GAKUTO Inter. Ser., Math. Sci. Appl., 29 (2008), 211-226.
[4]	Z. Szymańska, J. Urbański and A. Marciniak-Czochra, Mathematical modelling of the influence of heat shock proteins on cancer invasion of tissue, J. Math. Biol., 58 (2009), 819-844. doi: 10.1007/s00285-008-0220-0.

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References:

[1]	A. Ito, K. Yamamoto, Y. Yanagi and K. Hosono, Key-pathway analysis in biochemical reaction of HSP synthesis process, Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, Okayama, Japan, March 26-29, (2009), 474-479. doi: 10.1109/ICNSC.2009.4919322.
[2]	T. R. Rieger, R. I. Morimoto and V. Hatzimanikatis, Mathematical modeling of the eukaryotic heat-shock response: Dynamics of the HSP70 promoter, Biophysical Journal, 88 (2005), 1646-1658. doi: 10.1529/biophysj.104.055301.
[3]	Y. Yanagi and A. Ito, Numerical simulations of heat shock protein synthesis and tumor invasion phenimenon, GAKUTO Inter. Ser., Math. Sci. Appl., 29 (2008), 211-226.
[4]	Z. Szymańska, J. Urbański and A. Marciniak-Czochra, Mathematical modelling of the influence of heat shock proteins on cancer invasion of tissue, J. Math. Biol., 58 (2009), 819-844. doi: 10.1007/s00285-008-0220-0.

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