×

Why is evolution important in cancer and what mathematics should be used to treat cancer? Focus on drug resistance. (English) Zbl 1404.92087

Mondaini, Rubem P. (ed.), Trends in biomathematics: modeling, optimization and computational problems. Selected works from the 17th BIOMAT consortium lectures, Moscow, Russia, October 30 – November 3, 2017. Cham: Springer; Rio de Janeiro: BIOMAT Consortium, International Institute for Interdisciplinary Sciences (ISBN 978-3-319-91091-8/hbk; 978-3-319-91092-5/ebook). 107-120 (2018).
Summary: The clinical question of drug resistance in cancer, our initial motivation to study continuous models of adaptive cell population dynamics, leads naturally and more generally to consider the cancer disease itself from an evolutionary biology viewpoint, a consideration without which even the best targeted therapies will likely most often eventually fail. Among the challenging questions to mathematicians who tackle the task of understanding this disease and optimising its treatment are the representation of phenotypic heterogeneity of cancer cell populations and of their plasticity in response to anticancer drug insults. Such representation can be obtained using phenotype-structured models of healthy and cancer cell populations, and optimal control methods to optimise drug effects, with the perspective to implement them in the therapeutics of cancer, aiming at both avoiding the emergence of drug resistance in tumours and taking into account a constraint of limiting unwanted adverse effects to healthy tissues.
For the entire collection see [Zbl 1401.92005].

MSC:

92C50 Medical applications (general)
92D15 Problems related to evolution
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] S. Benzekry, Ph. Hahnfeldt, J. Theor. Biol. 335, 235 (2013) · Zbl 1397.92312 · doi:10.1016/j.jtbi.2013.06.036
[2] F. Billy, J. Clairambault, Discr. Cont. Dyn. Syst. Ser. B 18, 865 (2013) · Zbl 1277.92010 · doi:10.3934/dcdsb.2013.18.865
[3] H.M. Byrne, D. Drasdo, J. Math. Biol. 58, 657 (2009) · Zbl 1311.92060 · doi:10.1007/s00285-008-0212-0
[4] C. Carrère, J. Theor. Biol. 413, 24 (2017) · Zbl 1368.92081 · doi:10.1016/j.jtbi.2016.11.009
[5] R.H. Chisholm, T. Lorenzi, A. Lorz, A.K. Larsen, L. Almeida, A. Escargueil, J. Clairambault, Cancer Res. 75, 930 (2015) · doi:10.1158/0008-5472.CAN-14-2103
[6] R.H. Chisholm, T. Lorenzi, J. Clairambault, Biochem. Biophys. Acta Gen. Subj. 1860, 2627 (2016) · doi:10.1016/j.bbagen.2016.06.009
[7] R.H. Chisholm, T. Lorenzi, A. Lorz, Commun. Math. Sci. 14, 1181 (2016) · Zbl 1344.35155 · doi:10.4310/CMS.2016.v14.n4.a16
[8] R.H. Chisholm, T. Lorenzi, L. Desvillettes, B.D. Hughes, Z. Angew. Math. Phys. 67:100, 1 (2016)
[9] P.C.W. Davies, C.H. Lineweaver, Phys. Biol. 7, 1 (2011)
[10] M. Gerlinger et al., N. Engl. J. Med. 336, 883 (2012) · doi:10.1056/NEJMoa1113205
[11] R.J. Gillies, D. Verduzco, R.A. Gatenby, Nat. Rev. Cancer 12, 487 (2012) · doi:10.1038/nrc3298
[12] A. Goldman, M. Kohandel, J. Clairambault, Curr. Stem Cell Rep. 3, 253 (2017) · doi:10.1007/s40778-017-0097-1
[13] A. Goldman, M. Kohandel, J. Clairambault, Curr. Stem Cell Rep. 3, 260 (2017) · doi:10.1007/s40778-017-0098-0
[14] M.M. Gottesman, T. Fojo, S.E. Bates. Nat. Rev. Cancer 2, 48 (2002) · doi:10.1038/nrc706
[15] S. Huang, Semin. Cancer Biol. 21, 183 (2011) · doi:10.1016/j.semcancer.2011.05.003
[16] S. Huang, Cancer Metastasis Rev. 32, 423 (2013) · doi:10.1007/s10555-013-9435-7
[17] S. Huang, Y.P. Guo, G. May, T. Enver, Dev. Biol. 305, 695 (2007) · doi:10.1016/j.ydbio.2007.02.036
[18] F. Jacob, Science 196, 1161 (1977) · doi:10.1126/science.860134
[19] U. Łedżewicz, H. Schättler, Discr. Cont. Dyn. Syst. Ser. B 6, 129 (2006)
[20] U. Łedżewicz, H. Schättler, \(Mathematical Models of Tumor-Immune Dynamics\) (Springer, New York, 2013), p. 157
[21] Y. Li, J. Laterra, Cancer Res. 72, 576 (2012) · doi:10.1158/0008-5472.CAN-11-3070
[22] A. Lorz, T. Lorenzi, J. Clairambault, A. Escargueil, B. Perthame, Bull. Math. Biol. 77, 1 (2015) · Zbl 1334.92204 · doi:10.1007/s11538-014-0046-4
[23] S.E. Luria, M. Delbrück, Genetics 28, 491 (1943)
[24] E. Pasquier, M. Kavallaris, N. André, Nat. Rev. Clin. Oncol. 7, 455 (2010) · doi:10.1038/nrclinonc.2010.82
[25] B. Perthame, \(Transport Equations in Biology\) (Birkhäuser, Basel, 2007) · Zbl 1185.92006
[26] T. Philippi, J. Seger, Tends Ecol. Evol. 4, 41 (1989) · doi:10.1016/0169-5347(89)90138-9
[27] C. Pouchol, Modelling interactions between tumour cells and supporting adipocytes in breast cancer. https://hal.inria.fr/hal-01252122 (2015)
[28] C. Pouchol, E. Trélat, arXiv 1702.06187. https://hal.inria.fr/hal-01618357 (2017)
[29] C. Pouchol, J. Clairambault, A. Lorz, E. Trélat, arXiv 1612.04698 (2016); J. Maths Pures Appl. (2017, to appear)
[30] S.M. Shaffer et al., Nature 546, 431 (2017) · doi:10.1038/nature22794
[31] S.V. Sharma et al., Cell 141, 69 (2010) · doi:10.1016/j.cell.2010.02.027
[32] E. Trélat, \(Contrôle Optimal\) (Vuibert, Paris, 2005), 246 pp. Reviewed in Mathscinet MR2224013, 2007f:49001
[33] B. Ujvari, B. Roche, F. Thomas (eds.), \(Ecology and Evolution of Cancer\) (Academic, London, 2017)
[34] C.H. Waddington, \(The Strategy of Genes\) (George Allen & Unwin, London, 1957)
[35] A. Wu et al., Proc. Natl. Acad. Sci. USA 112, 10467 (2015) · doi:10.1073/pnas.1512396112
[36] L. Zitvogel, L. Apetoh, F. Ghiringhelli, G. Kroemer, Nat. Rev. Immunol. 8, 59 (2008) · doi:10.1038/nri2216
[37] L. Zitvogel, O. Kepp, G. Kroemer, Nat. Rev. Clin. Oncol. 8, 151 (2011) · doi:10.1038/nrclinonc.2010.223
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.