2013, 10(5&6): 1501-1518. doi: 10.3934/mbe.2013.10.1501

Data and implication based comparison of two chronic myeloid leukemia models

1. 

School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, United States, United States

2. 

Department of Mathematics, North Carolina State University, Raleigh, NC 27695, United States

3. 

School of Mathematics and Statistical Sciences, Arizona State University, Tempe, AZ 85281

Received  October 2012 Revised  January 2013 Published  August 2013

Chronic myeloid leukemia, a disorder of hematopoietic stem cells, is currently treated using targeted molecular therapy with imatinib. We compare two models that describe the treatment of CML, a multi-scale model (Model 1) and a simple cell competition model (Model 2). Both models describe the competition of leukemic and normal cells, however Model 1 also describes the dynamics of BCR-ABL, the oncogene targeted by imatinib, at the sub-cellular level. Using clinical data, we analyze the differences in estimated parameters between the models and the capacity for each model to predict drug resistance. We found that while both models fit the data well, Model 1 is more biologically relevant. The estimated parameter ranges for Model 2 are unrealistic, whereas the parameter ranges for Model 1 are close to values found in literature. We also found that Model 1 predicts long-term drug resistance from patient data, which is exhibited by both an increase in the proportion of leukemic cells as well as an increase in BCR-ABL/ABL%. Model 2, however, is not able to predict resistance and accurately model the clinical data. These results suggest that including sub-cellular mechanisms in a mathematical model of CML can increase the accuracy of parameter estimation and may help to predict long-term drug resistance.
Citation: R. A. Everett, Y. Zhao, K. B. Flores, Yang Kuang. Data and implication based comparison of two chronic myeloid leukemia models. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1501-1518. doi: 10.3934/mbe.2013.10.1501
References:
[1]

L. H. Abbott and F. Michor, Mathematical models of targeted cancer therapy,, British Journal of Cancer, 95 (2006), 1136.   Google Scholar

[2]

S. Brandford, Z. Rudzki, A. Grigg, J. F. Seymour, K. Taylor, R. Herrmann, C. Arthur, J. Szer and K. Lynch, The incidence of BCR-ABL kinase mutations in chronic myeloid leukemia patients is as high in the second year of imatinib therapy as the first but survival after mutation detection is significantly longer for patients with mutations detected in the second year of therapy,, BLOOD, 102 (2003).   Google Scholar

[3]

M. D. Charles and L. Sawyers, Chronic myeloid leukemia,, The New England Journal of Medicine, 340 (1999), 1330.   Google Scholar

[4]

J. Foo, M. W. Drummond, B. Clarkson, T. Holyoake and F. Michor, Eradication of chronic myeloid leukemia stem cells: A novel mathematical model predicts no therapeutic benefit of adding G-CSF to imatinib,, PLoS Computational Biology, 5 (2009), 1.   Google Scholar

[5]

D. Frame, Chronic myeloid leukemia: Standard treatment options,, American Journal of Health-System Pharmacy, 63 (2006).   Google Scholar

[6]

M. E. Gorre, M. Mohammed, K. Ellwood, N. Hsu, R. Paquette, P. Nagesh Rao and C. L. Sawyers, Clinical resistance to STI-571 cancer therapy caused by BCR-ABL gene mutation or amplification,, Science, 293 (2001), 876.   Google Scholar

[7]

I. J. Griswold, M. MacPartline, T. Bumm, V. L. Goss, T. O'Hare, K. A. Lee, A. S. Corbin, E. P. Stoffregen, C. Smith, K. Johnson, E. M. Moseson, L. J. Wood, R. D. Polakiewicz, B. J. Druker and M. W. Deininger, Kinase domain mutants of bcr-abl exhibit altered transformation potency, kinase activity, and substrate utilization, irrespective of sensitivity to imatinib,, Molecular and Cellular Biology, 26 (2006), 6082.   Google Scholar

[8]

J. Jelinek, V. Gharibyan, M. Estecio, K. Kondo, R. He, W. Chung, Y. Lu, N. Zhang, S. Liang, H. Kantarjian, J. Cortes and J-P. Issa, Aberrant DNA methylation is associated with disease progression, resistance to imatinib and shortened survival in chronic myelogenous leukemia,, PLoS ONE, 6 (2011).   Google Scholar

[9]

I. Kareva, F. Berezovskaya and C. Castillo-Chavez, Myeloid cells in tumour-immune interactions,, Journal of Biological Dynamics, 4 (2010), 315.  doi: 10.1080/17513750903261281.  Google Scholar

[10]

N. L. Komarova and D. Wodarz, Effect of cellular quiescence on the success of targeted CML therapy,, PLoS ONE, 2 (2007).   Google Scholar

[11]

F. Michor, Reply: The long-term response to imatinib treatment of CML,, Biritish Journal of Cancer, 96 (2007), 697.   Google Scholar

[12]

F. Michor, Quantitative approaches to analyzing imatinib-treated chronic myeloid leukemia,, TRENDS in Pharmacological Sciences, 28 (2007), 197.   Google Scholar

[13]

F. Michor, T. P. Hughes, Y. Iwasa, S. Branford, N. P. Shah, C. L. Sawyers and M. A. Nowak, Dynamics of chronic myeloid leukemia,, Nature, 435 (2005), 1267.   Google Scholar

[14]

M. C. Muller, N. Gattermann, T. Lahaye, M. W. N. Deininger, A. Berndt, S. Fruehauf, A. Neubauer, T. Fischer, D. K. Hossfeld, F. Schneller, S. W. Krause, C. Nerl, H. G. Sayer, O. G. Ottmann, C. Waller, W. Aulitzky, P. le Coutre, M. Freund, K. Merx, P. Paschka, H. Konig, S. Kreil, U. Berger, H. Gschaidmeier, R. Hehlmann and A. Hochhaus, Dynamics of BCR-ABL mRNA expression in first-line therapy of chronic myelogenous leukemia patients with imatinib or interferon a/ara-C,, Leukemia, 17 (2003), 2392.   Google Scholar

[15]

C. Nishioka, T. Ikezoe, K. Udaka and A. Yokoyama, Imatinib causes epigenetic alterations of PTEN gene via upregulation of DNA methyltransferases and polycomb group proteins,, Blood Cancer Journal, 1 (2011).   Google Scholar

[16]

T. Portz, Y. Kuang and J. D. Nagy, A clinical data validated mathematical model of prostate cancer growth under intermittent androgen suppression therapy,, AIP Advances, 2 (2012).   Google Scholar

[17]

I. Roeder, M. Horn, I. Glauche, A. Hochhaus, M. C Mueller and M. Loeffler, Dynamic modeling of imatinib-treated chronic myeloid leukemia: Functional insights and clinical implications,, Nature Medicine, 12 (2006), 1181.   Google Scholar

[18]

A. M. Stein, D. Bottino, V. Modur, S. Branford, J. Kaeda, J. M. Goldman, T. P. Hughes, J. P. Radich and A. Hochhaus, BCR-ABL transcript dynamics support the hypothesis that leukemic stem cells are reduced during imatinib treatment,, Clinical Cancer Research, 17 (2011), 6812.   Google Scholar

show all references

References:
[1]

L. H. Abbott and F. Michor, Mathematical models of targeted cancer therapy,, British Journal of Cancer, 95 (2006), 1136.   Google Scholar

[2]

S. Brandford, Z. Rudzki, A. Grigg, J. F. Seymour, K. Taylor, R. Herrmann, C. Arthur, J. Szer and K. Lynch, The incidence of BCR-ABL kinase mutations in chronic myeloid leukemia patients is as high in the second year of imatinib therapy as the first but survival after mutation detection is significantly longer for patients with mutations detected in the second year of therapy,, BLOOD, 102 (2003).   Google Scholar

[3]

M. D. Charles and L. Sawyers, Chronic myeloid leukemia,, The New England Journal of Medicine, 340 (1999), 1330.   Google Scholar

[4]

J. Foo, M. W. Drummond, B. Clarkson, T. Holyoake and F. Michor, Eradication of chronic myeloid leukemia stem cells: A novel mathematical model predicts no therapeutic benefit of adding G-CSF to imatinib,, PLoS Computational Biology, 5 (2009), 1.   Google Scholar

[5]

D. Frame, Chronic myeloid leukemia: Standard treatment options,, American Journal of Health-System Pharmacy, 63 (2006).   Google Scholar

[6]

M. E. Gorre, M. Mohammed, K. Ellwood, N. Hsu, R. Paquette, P. Nagesh Rao and C. L. Sawyers, Clinical resistance to STI-571 cancer therapy caused by BCR-ABL gene mutation or amplification,, Science, 293 (2001), 876.   Google Scholar

[7]

I. J. Griswold, M. MacPartline, T. Bumm, V. L. Goss, T. O'Hare, K. A. Lee, A. S. Corbin, E. P. Stoffregen, C. Smith, K. Johnson, E. M. Moseson, L. J. Wood, R. D. Polakiewicz, B. J. Druker and M. W. Deininger, Kinase domain mutants of bcr-abl exhibit altered transformation potency, kinase activity, and substrate utilization, irrespective of sensitivity to imatinib,, Molecular and Cellular Biology, 26 (2006), 6082.   Google Scholar

[8]

J. Jelinek, V. Gharibyan, M. Estecio, K. Kondo, R. He, W. Chung, Y. Lu, N. Zhang, S. Liang, H. Kantarjian, J. Cortes and J-P. Issa, Aberrant DNA methylation is associated with disease progression, resistance to imatinib and shortened survival in chronic myelogenous leukemia,, PLoS ONE, 6 (2011).   Google Scholar

[9]

I. Kareva, F. Berezovskaya and C. Castillo-Chavez, Myeloid cells in tumour-immune interactions,, Journal of Biological Dynamics, 4 (2010), 315.  doi: 10.1080/17513750903261281.  Google Scholar

[10]

N. L. Komarova and D. Wodarz, Effect of cellular quiescence on the success of targeted CML therapy,, PLoS ONE, 2 (2007).   Google Scholar

[11]

F. Michor, Reply: The long-term response to imatinib treatment of CML,, Biritish Journal of Cancer, 96 (2007), 697.   Google Scholar

[12]

F. Michor, Quantitative approaches to analyzing imatinib-treated chronic myeloid leukemia,, TRENDS in Pharmacological Sciences, 28 (2007), 197.   Google Scholar

[13]

F. Michor, T. P. Hughes, Y. Iwasa, S. Branford, N. P. Shah, C. L. Sawyers and M. A. Nowak, Dynamics of chronic myeloid leukemia,, Nature, 435 (2005), 1267.   Google Scholar

[14]

M. C. Muller, N. Gattermann, T. Lahaye, M. W. N. Deininger, A. Berndt, S. Fruehauf, A. Neubauer, T. Fischer, D. K. Hossfeld, F. Schneller, S. W. Krause, C. Nerl, H. G. Sayer, O. G. Ottmann, C. Waller, W. Aulitzky, P. le Coutre, M. Freund, K. Merx, P. Paschka, H. Konig, S. Kreil, U. Berger, H. Gschaidmeier, R. Hehlmann and A. Hochhaus, Dynamics of BCR-ABL mRNA expression in first-line therapy of chronic myelogenous leukemia patients with imatinib or interferon a/ara-C,, Leukemia, 17 (2003), 2392.   Google Scholar

[15]

C. Nishioka, T. Ikezoe, K. Udaka and A. Yokoyama, Imatinib causes epigenetic alterations of PTEN gene via upregulation of DNA methyltransferases and polycomb group proteins,, Blood Cancer Journal, 1 (2011).   Google Scholar

[16]

T. Portz, Y. Kuang and J. D. Nagy, A clinical data validated mathematical model of prostate cancer growth under intermittent androgen suppression therapy,, AIP Advances, 2 (2012).   Google Scholar

[17]

I. Roeder, M. Horn, I. Glauche, A. Hochhaus, M. C Mueller and M. Loeffler, Dynamic modeling of imatinib-treated chronic myeloid leukemia: Functional insights and clinical implications,, Nature Medicine, 12 (2006), 1181.   Google Scholar

[18]

A. M. Stein, D. Bottino, V. Modur, S. Branford, J. Kaeda, J. M. Goldman, T. P. Hughes, J. P. Radich and A. Hochhaus, BCR-ABL transcript dynamics support the hypothesis that leukemic stem cells are reduced during imatinib treatment,, Clinical Cancer Research, 17 (2011), 6812.   Google Scholar

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