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

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

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.
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 & 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, (2009), 26. 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. 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., 29 (2008), 211.

[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. doi: 10.1007/s00285-008-0220-0.

show all references

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, (2009), 26. 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. 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., 29 (2008), 211.

[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. doi: 10.1007/s00285-008-0220-0.

[1]

Massimiliano Guzzo, Giancarlo Benettin. A spectral formulation of the Nekhoroshev theorem and its relevance for numerical and experimental data analysis. Discrete & Continuous Dynamical Systems - B, 2001, 1 (1) : 1-28. doi: 10.3934/dcdsb.2001.1.1

[2]

Michael V. Klibanov, Loc H. Nguyen, Anders Sullivan, Lam Nguyen. A globally convergent numerical method for a 1-d inverse medium problem with experimental data. Inverse Problems & Imaging, 2016, 10 (4) : 1057-1085. doi: 10.3934/ipi.2016032

[3]

Ahuod Alsheri, Ebraheem O. Alzahrani, Asim Asiri, Mohamed M. El-Dessoky, Yang Kuang. Tumor growth dynamics with nutrient limitation and cell proliferation time delay. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3771-3782. doi: 10.3934/dcdsb.2017189

[4]

Franco Flandoli, Matti Leimbach. Mean field limit with proliferation. Discrete & Continuous Dynamical Systems - B, 2016, 21 (9) : 3029-3052. doi: 10.3934/dcdsb.2016086

[5]

Graeme Wake, Anthony Pleasants, Alan Beedle, Peter Gluckman. A model for phenotype change in a stochastic framework. Mathematical Biosciences & Engineering, 2010, 7 (3) : 719-728. doi: 10.3934/mbe.2010.7.719

[6]

Diana M. Thomas, Ashley Ciesla, James A. Levine, John G. Stevens, Corby K. Martin. A mathematical model of weight change with adaptation. Mathematical Biosciences & Engineering, 2009, 6 (4) : 873-887. doi: 10.3934/mbe.2009.6.873

[7]

Joana Terra, Noemi Wolanski. Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data. Discrete & Continuous Dynamical Systems - A, 2011, 31 (2) : 581-605. doi: 10.3934/dcds.2011.31.581

[8]

Tuan Phung-Duc, Ken'ichi Kawanishi. Multiserver retrial queue with setup time and its application to data centers. Journal of Industrial & Management Optimization, 2018, 13 (5) : 1-21. doi: 10.3934/jimo.2018030

[9]

Kazufumi Ito, Karim Ramdani, Marius Tucsnak. A time reversal based algorithm for solving initial data inverse problems. Discrete & Continuous Dynamical Systems - S, 2011, 4 (3) : 641-652. doi: 10.3934/dcdss.2011.4.641

[10]

Loïc Bourdin, Emmanuel Trélat. Optimal sampled-data control, and generalizations on time scales. Mathematical Control & Related Fields, 2016, 6 (1) : 53-94. doi: 10.3934/mcrf.2016.6.53

[11]

Eduard Feireisl, Hana Petzeltová, Konstantina Trivisa. Multicomponent reactive flows: Global-in-time existence for large data. Communications on Pure & Applied Analysis, 2008, 7 (5) : 1017-1047. doi: 10.3934/cpaa.2008.7.1017

[12]

Koray Karabina, Berkant Ustaoglu. Invalid-curve attacks on (hyper)elliptic curve cryptosystems. Advances in Mathematics of Communications, 2010, 4 (3) : 307-321. doi: 10.3934/amc.2010.4.307

[13]

Robert L. Devaney, Daniel M. Look. Buried Sierpinski curve Julia sets. Discrete & Continuous Dynamical Systems - A, 2005, 13 (4) : 1035-1046. doi: 10.3934/dcds.2005.13.1035

[14]

Hans-Christoph Grunau, Guido Sweers. A clamped plate with a uniform weight may change sign. Discrete & Continuous Dynamical Systems - S, 2014, 7 (4) : 761-766. doi: 10.3934/dcdss.2014.7.761

[15]

M. Núñez-López, J. X. Velasco-Hernández, P. A. Marquet. The dynamics of technological change under constraints: Adopters and resources. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3299-3317. doi: 10.3934/dcdsb.2014.19.3299

[16]

L. Aguirre, P. Seibert. Types of change of stability and corresponding types of bifurcations. Discrete & Continuous Dynamical Systems - A, 1999, 5 (4) : 741-752. doi: 10.3934/dcds.1999.5.741

[17]

John D. Nagy, Dieter Armbruster. Evolution of uncontrolled proliferation and the angiogenic switch in cancer. Mathematical Biosciences & Engineering, 2012, 9 (4) : 843-876. doi: 10.3934/mbe.2012.9.843

[18]

Yangjin Kim, Soyeon Roh. A hybrid model for cell proliferation and migration in glioblastoma. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : 969-1015. doi: 10.3934/dcdsb.2013.18.969

[19]

Mostafa Adimy, Fabien Crauste, Laurent Pujo-Menjouet. On the stability of a nonlinear maturity structured model of cellular proliferation. Discrete & Continuous Dynamical Systems - A, 2005, 12 (3) : 501-522. doi: 10.3934/dcds.2005.12.501

[20]

Avner Friedman, Yangjin Kim. Tumor cells proliferation and migration under the influence of their microenvironment. Mathematical Biosciences & Engineering, 2011, 8 (2) : 371-383. doi: 10.3934/mbe.2011.8.371

2017 Impact Factor: 0.561

Metrics

  • PDF downloads (3)
  • HTML views (0)
  • Cited by (0)

[Back to Top]