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Stochastic Cellular Automata Model of Tumorous Neurosphere Growth: Roles of Developmental Maturity and Cell Death

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Stochastic Cellular Automata Model of Tumorous Neurosphere Growth: Roles of Developmental Maturity and Cell Death Journal of Theoretical Biology 467 (2019) 100–110 Contents lists available at ScienceDirect Journal of Theoretical Biology journal homepage: www.elsevier.com/locate/jtb Stochastic cellular automata model of tumorous neurosphere growth: Roles of developmental maturity and cell death ∗ Günther K.H. Zupanc a, , Frederick B. Zupanc a, Rifat Sipahi b a Laboratory of Neurobiology, Department of Biology, Northeastern University, Boston, MA, USA b Complex Dynamic Systems and Control Laboratory, Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA, USA a r t i c l e i n f o a b s t r a c t Article history: The neurosphere assay is a powerful in vitro system for studying stem/progenitor-cell-driven tissue Received 10 July 2018 growth. By employing a stochastic cellular automata model, we simulated the development of tumorous Revised 13 December 2018 neurospheres in response to transformation of a randomly selected progenitor cell into a brain tumor Accepted 19 January 2019 stem cell. Simulated tumorous neurospheres were distinguished from normal neurospheres by their Available online 29 January 2019 size, which exceeded that of normal neurospheres typically manifold. A decisive factor that determined Keywords: whether brain tumor stem cells gave rise to tumorous neurospheres was their ability to escape en- Neural stem/progenitor cells capsulation by neighboring cells, which suppressed mitotic activity through contact inhibition. In our Brain tumor stem cells simulations, the likelihood of tumorigenesis was strongly negatively correlated with the developmental Neurosphere assay maturity of the neurospheres in which the transformation of a progenitor cell into a brain tumor stem Tumor growth cell was induced. This likelihood was furthermore modulated by the probability of the progeny of Theoretical modeling dividing cells to undergo cell death. In developmentally immature neurospheres, the number of normal neurospheres, relative to the number of tumorous neurospheres, increased with increasing cell death probability. Markedly, in developmentally mature neurospheres the opposite effect was observed. This dichotomous effect of cell death on simulated tumor progression provides theoretical support for the seemingly paradoxical finding made by other authors in experimental studies that anti-cancer therapies based on induction of apoptosis may both promote and suppress tumor growth. ©2019 Elsevier Ltd. All rights reserved. 1. Introduction ( Sanai et al., 2005; Vescovi et al., 2006 ), an anatomical structure comprising the lining of the lateral ventricles. The NSPCs in the Brain tumors are relatively rare, yet they include some of the subventricular zone are a subpopulation of the astrocytes in this most lethal tumor types. Glioblastoma multiforme, an extremely region ( Doetsch et al., 1999 ). These stem cells generate transiently aggressive malignant primary brain tumor, has an incidence rate dividing progenitor cells, which, unlike their mother cells, have a of approximately 3 per 10 0,0 0 0 persons per year ( Tamimi and limited proliferative potential in vivo ( Ponti et al., 2013 ). Further- Juweid, 2017 ), thus accounting for less than 1% of all new cases of more, the progenitors produce neurons or glia, but not both, like cancer projected to occur in the United States in 2018 ( Siegel et al., done by adult neural stem cells. 2018 ). Despite considerable research and clinical treatment trials Sanai and co-authors have argued that the adult neural stem over the past few decades, prognosis of this glioma has remained cells and their progenitors are particularly susceptible to tumor poor. In untreated patients, the median survival time after diagno- transformation because they possess already the activated cellular sis is just 3–4 months ( Omuro and DeAngelis, 2013 ). When treated and molecular machinery required for mitotic division ( Sanai et al., with a combination of surgery, radiotherapy, and chemotherapy, 2005 ). They might, therefore, require less mutations than the 4–7 median survival is still only 15 months ( Stupp et al., 2005 ). thought to be needed for malignant transformation of a differenti- The cellular origin of gliomas, including glioblastoma, remains ated cell into a tumor cell ( Hanahan and Weinberg, 20 0 0 ). a matter of controversy. The currently prevalent hypothesis pro- One of the most valuable tools for studying NSPCs and poses that gliomas originate from adult neural stem cells and/or their progeny has been the neurosphere assay ( Reynolds and their progenitor cells (NSPCs), harbored in the subventricular zone Weiss, 1992 ). The clonal clusters of cells formed in this in-vitro system under serum-free conditions are referred to as neuro- spheres. By growth factor withdrawal and addition of serum to ∗ Corresponding author. the culture medium, they can be induced to differentiate into the E-mail address: [email protected] (G.K.H. Zupanc). https://doi.org/10.1016/j.jtbi.2019.01.028 0022-5193/© 2019 Elsevier Ltd. All rights reserved. G.K.H. Zupanc, F.B. Zupanc and R. Sipahi / Journal of Theoretical Biology 467 (2019) 100–110 101 three major types of cells of the central nervous system —neurons, cells. Using this approach, we have specifically examined how astrocytes, and oligodendrocytes. developmental maturity of the tissue, and cell death occurring at The neurosphere assay has been instrumental in obtaining different stages of maturity, affect tumorigenesis. evidence for the existence in glioblastoma multiforme of cells We have chosen CA modeling over other approaches because that exhibit the critical properties of stem cells ( Galli et al., 2004; it is particularly well suited to adequately represent, through its Ignatova et al., 2002 ). Cells from patients diagnosed with glio- array of cells, the discrete nature of individual cells in biological blastoma form clones under the growth conditions of this in-vitro tissue; and, through if-conditions and probabilities, rule-driven system. While they give rise only to astroglia in vivo, they have biological mechanisms that govern cellular events, such as cell pro- revealed multilineage potential under cell-culture conditions by liferation, cell migration, and cellular differentiation (for reviews, demonstrating their capability of producing neurons, astroglial, see Jones and Chapman, 2012; Newgreen et al., 2013 ). Taking ad- and oligodendroglia. Most importantly, when transplanted into the vantage of these features, this approach has been used successfully striatum of adult immunodeficient mice, they can induce tumors in previous studies of tumor growth (e.g., Alemani et al., 2012; closely resembling glioblastoma multiforme in humans ( Galli et al., Escobar Ospina and Perdomo, 2013; Monteagudo and Santos, 2004 ). Based on this evidence, these cells have been termed brain 2015; Oduola and Li, 2018; Sabzpoushan and Pourhasanzade, 2018; tumor stem cells (BTSCs). Santos and Monteagudo, 2015; Shrestha et al., 2013 ). Since the initial identification of BTSCs, a wealth of experi- mental data has been accumulated, particularly on the signaling 2. Model development pathways involved in initiation by these stem cells of malignant brain tumors and their propagation. Selective targeting of these 2.1. General structure of the CA model pathways, with the aim to eradicate the BTSCs, has led to the development of promising novel therapies ( Schonberg et al., 2014; The CA model used in the present study is a modified ver- Zhou et al., 2009 ). Nevertheless, there is a significant lack of sion of the model developed previously to simulate the growth of theoretical understanding of the cellular dynamics underlying neurospheres based on the proliferation of NSPCs ( Sipahi and Zu- BTSC-driven tumor initiation and growth. panc, 2018 ). As mentioned in the Introduction, the major difference Recently, we developed a stochastic cellular automata (CA) of the current model, compared to the previous version, is that it model to examine the role of various cellular phenomena, in- incorporates the possibility of a simulated progenitor cell to trans- cluding proliferative potential, contact inhibition, cell death, and form into a BTSC ( Fig. 1 ; Table 1 ). Model rules were programmed phagocytosis of dead cells, on growth rate, size, and composition in MATLAB ver. 2013a. In the following, we will describe the core of neurospheres ( Sipahi and Zupanc, 2018 ). Based on this model features of the current model. of normal neurosphere growth, we present, in the current study, a The model was constructed on the ( x, y ) plane, with dimen- modified CA model that incorporates transformation of progenitor sions of L x × L y , where L x = L y = 200 ( Table 2 ). The resulting plane cells into BTSCs, and subsequent propagation of the transformed was divided into squared lattices of unit edge length, yielding a Fig. 1. Flow chart of algorithm used to initiate and regulate simulated neurosphere growth. Solid lines are associated with generation, development, and death of cells, as well as clearance of dead corpses. Dashed lines indicate influences on decisions. The colors used for the different cell types is identical to the color coding applied to snapshots of neurospheres in Figs. 2–5 . Red , stem cell; orange , progenitor cell; green , brain tumor stem cell; blue , differentiated cell; black , dead cell. The encircled numbers indicate critical steps in the processes (see text for details). 102 G.K.H. Zupanc, F.B. Zupanc and R. Sipahi / Journal of Theoretical Biology 467 (2019)
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