Identifying the spatial and temporal dynamics of molecularly-distinct glioblastoma sub-populations

Bethan Morris; Lee Curtin; Andrea Hawkins-Daarud; Matthew E. Hubbard; Ruman Rahman; Stuart J. Smith; Dorothee Auer; Nhan L. Tran; Leland S. Hu; Jennifer M. Eschbacher; Kris A. Smith; Ashley Stokes; Kristin R. Swanson; Markus R. Owen; Bethan Morris; Lee Curtin; Andrea Hawkins-Daarud; Matthew E. Hubbard; Ruman Rahman; Stuart J. Smith; Dorothee Auer; Nhan L. Tran; Leland S. Hu; Jennifer M. Eschbacher; Kris A. Smith; Ashley Stokes; Kristin R. Swanson; Markus R. Owen

doi:10.3934/mbe.2020267

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 4905-4941. doi: 10.3934/mbe.2020267

Previous Article Next Article

Research article Special Issues

Identifying the spatial and temporal dynamics of molecularly-distinct glioblastoma sub-populations

1.
School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK
2.
Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, 85054, USA
3.
School of Medicine and Health Sciences, University of Nottingham, Nottingham, NG7 2UH, UK
4.
Department of Cancer Biology, Mayo Clinic, Phoenix, Arizona 85054, USA
5.
Department of Radiology, Mayo Clinic, Phoenix, Arizona 85054, USA
6.
Department of Pathology, Barrow Neurological Institute - St. Joseph’s Hospital and Medical Center, Phoenix, Arizona 85013, USA
7.
Department of Neurosurgery, Barrow Neurological Institute - St. Joseph’s Hospital and Medical Center, Phoenix, Arizona 85013, USA
8.
Department of Imaging Research, Barrow Neurological Institute - St. Joseph’s Hospital and Medical Center, Phoenix, Arizona 85013, USA
9.
Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona 85054, USA

Received: 01 April 2020 Accepted: 01 July 2020 Published: 16 July 2020

Glioblastomas (GBMs) are the most aggressive primary brain tumours and have no known cure. Each individual tumour comprises multiple sub-populations of genetically-distinct cells that may respond differently to targeted therapies and may contribute to disappointing clinical trial results. Image-localized biopsy techniques allow multiple biopsies to be taken during surgery and provide information that identifies regions where particular sub-populations occur within an individual GBM, thus providing insight into their regional genetic variability. These sub-populations may also interact with one another in a competitive or cooperative manner; it is important to ascertain the nature of these interactions, as they may have implications for responses to targeted therapies. We combine genetic information from biopsies with a mechanistic model of interacting GBM sub-populations to characterise the nature of interactions between two commonly occurring GBM sub-populations, those with EGFR and PDGFRA genes amplified. We study population levels found across image-localized biopsy data from a cohort of 25 patients and compare this to model outputs under competitive, cooperative and neutral interaction assumptions. We explore other factors affecting the observed simulated sub-populations, such as selection advantages and phylogenetic ordering of mutations, which may also contribute to the levels of EGFR and PDGFRA amplified populations observed in biopsy data.

Keywords:

Citation: Bethan Morris, Lee Curtin, Andrea Hawkins-Daarud, Matthew E. Hubbard, Ruman Rahman, Stuart J. Smith, Dorothee Auer, Nhan L. Tran, Leland S. Hu, Jennifer M. Eschbacher, Kris A. Smith, Ashley Stokes, Kristin R. Swanson, Markus R. Owen. Identifying the spatial and temporal dynamics of molecularly-distinct glioblastoma sub-populations[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 4905-4941. doi: 10.3934/mbe.2020267

Related Papers:

[1]	F. R. Guarguaglini, R. Natalini . Nonlinear transmission problems for quasilinear diffusion systems. Networks and Heterogeneous Media, 2007, 2(2): 359-381. doi: 10.3934/nhm.2007.2.359
[2]	Brahim Amaziane, Leonid Pankratov, Andrey Piatnitski . An improved homogenization result for immiscible compressible two-phase flow in porous media. Networks and Heterogeneous Media, 2017, 12(1): 147-171. doi: 10.3934/nhm.2017006
[3]	Steinar Evje, Kenneth H. Karlsen . Hyperbolic-elliptic models for well-reservoir flow. Networks and Heterogeneous Media, 2006, 1(4): 639-673. doi: 10.3934/nhm.2006.1.639
[4]	Francesca R. Guarguaglini . Stationary solutions and asymptotic behaviour for a chemotaxis hyperbolic model on a network. Networks and Heterogeneous Media, 2018, 13(1): 47-67. doi: 10.3934/nhm.2018003
[5]	Filipa Caetano, Martin J. Gander, Laurence Halpern, Jérémie Szeftel . Schwarz waveform relaxation algorithms for semilinear reaction-diffusion equations. Networks and Heterogeneous Media, 2010, 5(3): 487-505. doi: 10.3934/nhm.2010.5.487
[6]	Flavia Smarrazzo, Alberto Tesei . Entropy solutions of forward-backward parabolic equations with Devonshire free energy. Networks and Heterogeneous Media, 2012, 7(4): 941-966. doi: 10.3934/nhm.2012.7.941
[7]	Junlong Chen, Yanbin Tang . Homogenization of nonlinear nonlocal diffusion equation with periodic and stationary structure. Networks and Heterogeneous Media, 2023, 18(3): 1118-1177. doi: 10.3934/nhm.2023049
[8]	Zhangxin Chen . On the control volume finite element methods and their applications to multiphase flow. Networks and Heterogeneous Media, 2006, 1(4): 689-706. doi: 10.3934/nhm.2006.1.689
[9]	Markus Gahn, Maria Neuss-Radu, Peter Knabner . Effective interface conditions for processes through thin heterogeneous layers with nonlinear transmission at the microscopic bulk-layer interface. Networks and Heterogeneous Media, 2018, 13(4): 609-640. doi: 10.3934/nhm.2018028
[10]	Catherine Choquet, Ali Sili . Homogenization of a model of displacement with unbounded viscosity. Networks and Heterogeneous Media, 2009, 4(4): 649-666. doi: 10.3934/nhm.2009.4.649

Abstract

References

[1]	R. Stupp, W. P. Mason, M. J. Van Den Bent, M. Weller, B. Fisher, M. J. B. Taphoorn, et al., Radiotherapy plus concomitant and adjuvant temozolomide for glioblastoma, N. Engl. J. Med., 352 (2005), 987-996.
[2]	R. Stupp, M. E. Hegi, W. P. Mason, M. J. Van Den Bent, M. J. B. Taphoorn, R. C. Janzer, et al., Effects of radiotherapy with concomitant and adjuvant temozolomide versus radiotherapy alone on survival in glioblastoma in a randomised phase iii study: 5-year analysis of the eortc-ncic trial, Lancet Oncol., 10 (2009), 459-466.
[3]	R. Bonavia, W. K. Cavenee, F. B. Furnari, Heterogeneity maintenance in glioblastoma: a social network, Cancer Res., 71 (2011), 4055-4060.
[4]	Z. An, O. Aksoy, T. Zheng, Q.-W. Fan, W. A. Weiss, Epidermal growth factor receptor and egfrviii in glioblastoma: signaling pathways and targeted therapies, Oncogene, 37 (2018), 1561-1575.
[5]	M. Nakada, D. Kita, T. Watanabe, Y. Hayashi, J.-i. Hamada, The mechanism of chemoresistance against tyrosine kinase inhibitors in malignant glioma, Brain Tumor Pathol., 31 (2014), 198-207.
[6]	N. J. Szerlip, A. Pedraza, D. Chakravarty, M. Azim, J. McGuire, Y. Fang, et al., Intratumoral heterogeneity of receptor tyrosine kinases egfr and pdgfra amplification in glioblastoma defines subpopulations with distinct growth factor response, Proc. Natl. Acad. Sci. U.S.A., 109 (2012), 3041-3046. doi: 10.1073/pnas.1114033109
[7]	L. S. Hu, S. Ning, J. M. Eschbacher, L. C. Baxter, N. Gaw, S. Ranjbar, et al., Radiogenomics to characterize regional genetic heterogeneity in glioblastoma, Neuro-oncology, 19 (2017), 128-137.
[8]	S. J. Smith, M. Diksin, S. Chhaya, S. Sairam, M. A. Estevez-Cebrero, R. Rahman, The invasive region of glioblastoma defined by 5ala guided surgery has an altered cancer stem cell marker profile compared to central tumour, Int.J. Mol. Sci., 18 (2017), 2452.
[9]	A. Sottoriva, I. Spiteri, S. G. Piccirillo, A. Touloumis, V. P. Collins, J. C. Marioni, et al., Intratumor heterogeneity in human glioblastoma reflects cancer evolutionary dynamics, Proc. Natl. Acad. Sci. U.S.A., 110 (2013), 4009-4014.
[10]	J. G. Lyons, E. Lobo, A. M. Martorana, M. R. Myerscough, Clonal diversity in carcinomas: its implications for tumour progression and the contribution made to it by epithelial-mesenchymal transitions, Clin. Exp. Metastasis, 25 (2008), 665-677.
[11]	C. Lopez-Gines, R. Gil-Benso, R. Ferrer-Luna, R. Benito, E. Serna, J. Gonzalez-Darder, et al., New pattern of egfr amplification in glioblastoma and the relationship of gene copy number with gene expression profile, Mod. Pathol., 23 (2010), 856-865. doi: 10.1038/modpathol.2010.62
[12]	F. B. Furnari, T. F. Cloughesy, W. K. Cavenee, P. S. Mischel, Heterogeneity of epidermal growth factor receptor signalling networks in glioblastoma, Nat. Rev. Cancer, 15 (2015), 302.
[13]	B. R. Voldborg, L. Damstrup, M. Spang-Thomsen, H. S. Poulsen, Epidermal growth factor receptor (egfr) and egfr mutations, function and possible role in clinical trials, Ann. Oncol., 8 (1997), 1197-1206.
[14]	J. J. Parker, K. R. Dionne, R. Massarwa, M. Klaassen, N. K. Foreman, L. Niswander, et al., Gefitinib selectively inhibits tumor cell migration in egfr-amplified human glioblastoma, Neurooncology, 15 (2013), 1048-1057.
[15]	K. M. Talasila, A. Soentgerath, P. Euskirchen, G. V. Rosland, J. Wang, P. C. Huszthy, et al., Egfr wild-type amplification and activation promote invasion and development of glioblastoma independent of angiogenesis, Acta Neuropathol., 125 (2013), 683-698.
[16]	N. Shinojima, K. Tada, S. Shiraishi, T. Kamiryo, M. Kochi, H. Nakamura, et al., Prognostic value of epidermal growth factor receptor in patients with glioblastoma multiforme, Cancer Res., 63 (2003), 6962-6970.
[17]	A. Alentorn, Y. Marie, C. Carpentier, B. Boisselier, M. Giry, M. Labussiere, et al., Prevalence, clinico-pathological value, and co-occurrence of pdgfra abnormalities in diffuse gliomas, Neurooncology, 14 (2012), 1393-1403.
[18]	P. Blume-Jensen, T. Hunter, Oncogenic kinase signalling, Nature, 411 (2001), 355
[19]	Cancer Genome Atlas Research Network, Comprehensive genomic characterization defines human glioblastoma genes and core pathways, Nature, 455 (2008), 1061.
[20]	M. M. Lino, A. Merlo, Pi3kinase signaling in glioblastoma, J. Neurooncol., 103 (2011), 417-427.
[21]	M. Snuderl, L. Fazlollahi, L. P. Le, M. Nitta, B. H. Zhelyazkova, C. J. Davidson, et al., Mosaic amplification of multiple receptor tyrosine kinase genes in glioblastoma, Cancer Cell, 20 (2011), 810-817.
[22]	F. Chen, L. Ding, Co-survival of the fittest few: mosaic amplification of receptor tyrosine kinases in glioblastoma, Genome Biol., 13 (2012), 141.
[23]	M. J. Borad, M. D. Champion, J. B. Egan, W. S. Liang, R. Fonseca, A. H. Bryce, et al., Integrated genomic characterization reveals novel, therapeutically relevant drug targets in fgfr and egfr pathways in sporadic intrahepatic cholangiocarcinoma, PLoS Genet., 10, e1004135.
[24]	D. W. Craig, J. A. O'Shaughnessy, J. A. Kiefer, J. Aldrich, S. Sinari, T. M. Moses, et al., Genome and transcriptome sequencing in prospective metastatic triple-negative breast cancer uncovers therapeutic vulnerabilities, Mol. Cancer Ther., 12 (2013), 104-116.
[25]	R. Mehrian-Shai, M. Yalon, I. Moshe, I. Barshack, D. Nass, J. Jacob, et al., Identification of genomic aberrations in hemangioblastoma by droplet digital pcr and snp microarray highlights novel candidate genes and pathways for pathogenesis, BMC Genom., 17 (2016), 56.
[26]	J. C. L. Alfonso, K. Talkenberger, M. Seifert, B. Klink, A. Hawkins-Daarud, K. R. Swanson, et al., The biology and mathematical modelling of glioma invasion: a review, J. R. Soc. Interface, 14 (2017), 20170490.
[27]	K. R. Swanson, H. L. P. Harpold, D. L. Peacock, R. Rockne, C. Pennington, L. Kilbride, et al., Velocity of radial expansion of contrast-enhancing gliomas and the effectiveness of radiotherapy in individual patients: a proof of principle, Clin. Oncol., 20 (2008), 301-308. doi: 10.1016/j.clon.2008.01.006
[28]	K. R. Swanson, R. C. Rostomily, E. C. Alvord Jr, Confirmation of a theoretical model describing the relative contributions of net growth and dispersal in individual infiltrating gliomas, Can. J. Neurol. Sci., 30 (2003), 407-434.
[29]	K. R. Swanson, R. C. Rostomily, E. C. Alvord Jr, A mathematical modelling tool for predicting survival of individual patients following resection of glioblastoma: a proof of principle, Br. J. Cancer, 98 (2008), 113-119.
[30]	K. R. Swanson, E. C. Alvord, J. D. Murray, Virtual brain tumours (gliomas) enhance the reality of medical imaging and highlight inadequacies of current therapy, Br. J. Cancer, 86 (2002), 14-18.
[31]	K. R. Swanson, E. C. Alvord Jr, J. D. Murray, A quantitative model for differential motility of gliomas in grey and white matter, Cell Prolif., 33 (2000), 317-329.
[32]	K. R. Swanson, C. Bridge, J. D. Murray, E. C. Alvord Jr, Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion, J. Neurosci., 216 (2003), 1-10.
[33]	A. L. Baldock, S. Ahn, R. Rockne, S. Johnston, M. Neal, D. Corwin, et al., Patient-specific metrics of invasiveness reveal significant prognostic benefit of resection in a predictable subset of gliomas, PLoS One, 9, e99057.
[34]	P. R. Jackson, J. Juliano, A. Hawkins-Daarud, R. C. Rockne, K. R. Swanson, Patient-specific mathematical neuro-oncology: using a simple proliferation and invasion tumor model to inform clinical practice, Bull. Math. Biol., 77 (2015), 846-856.
[35]	C. H. Wang, J. K. Rockhill, M. Mrugala, D. L. Peacock, A. Lai, K. Jusenius, et al., Prognostic significance of growth kinetics in newly diagnosed glioblastomas revealed by combining serial imaging with a novel biomathematical model, Cancer Res., 69 (2009), 9133-9140.
[36]	K. J. Painter, T. Hillen, Volume-filling and quorum-sensing in models for chemosensitive movement, Can. Appl. Math. Quart, 10 (2002), 501-543.
[37]	P. Gerlee, S. Nelander, The impact of phenotypic switching on glioblastoma growth and invasion, PLoS Comput. Biol., 8, e1002556.
[38]	K. R. Swanson, R. C. Rockne, J. Claridge, M. A. Chaplain, E. C. Alvord, A. R. A. Anderson, Quantifying the role of angiogenesis in malignant progression of gliomas: in silico modeling integrates imaging and histology, Cancer Res., 71 (2011), 7366-7375.
[39]	S. M. Blower, H. Dowlatabadi, Sensitivity and uncertainty analysis of complex models of disease transmission: an hiv model, as an example, International Statistical Review/Revue Internationale de Statistique, 229-243.
[40]	A. Hawkins-Daarud, S. K. Johnston, K. R. Swanson, Quantifying uncertainty and robustness in a biomathematical model-based patient-specific response metric for glioblastoma, JCO Clin. Cancer Inform., 3 (2019), 1-8.
[41]	S. Marino, I. B. Hogue, C. J. Ray, D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology, J. Theor. Biol., 254 (2008), 178-196.
[42]	S. C. Massey, J. C. Urcuyo, B. M. Marin, J. N. Sarkaria, K. R. Swanson, Quantifying glioblastoma drug response dynamics incorporating resistance and blood brain barrier penetrance from experimental data, Front. Physiol., In Press.
[43]	C. A. Smith, C. A. Yates, The auxiliary region method: a hybrid method for coupling pde-and brownian-based dynamics for reaction-diffusion systems, Royal Soc. Open Sci., 5 (2018), 180920.

This article has been cited by:

1.	G. Bretti, R. Natalini, M. Ribot, A hyperbolic model of chemotaxis on a network: a numerical study, 2014, 48, 0764-583X, 231, 10.1051/m2an/2013098
2.	Elena Bonetti, Cecilia Cavaterra, Francesco Freddi, Maurizio Grasselli, Roberto Natalini, A nonlinear model for marble sulphation including surface rugosity and mechanical damage, 2023, 73, 14681218, 103886, 10.1016/j.nonrwa.2023.103886
3.	G. Frasca-Caccia, C. Valentino, F. Colace, D. Conte, An overview of differential models for corrosion of cultural heritage artefacts, 2023, 18, 0973-5348, 27, 10.1051/mmnp/2023031

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)