'Go or grow': the key to the emergence of invasion in tumour progression?

Mathematical Analysis of Glioma Growth in a Murine Model

Five immunocompetent C57BL/6-cBrd/cBrd/Cr (albino C57BL/6) mice were injected with GL261-luc2 cells, a cell line sharing characteristics of human glioblastoma multiforme (GBM). The mice were imaged using magnetic resonance (MR) at five separate time points to characterize growth and development of the tumor. After 25 days, the final tumor volumes of the mice varied from 12 mm³ to 62 mm³, even though mice were inoculated from the same tumor cell line under carefully controlled conditions. We generated hypotheses to explore large variances in final tumor size and tested them with our simple reaction-diffusion model in both a 3-dimensional (3D) finite difference method and a 2-dimensional (2D) level set method. The parameters obtained from a best-fit procedure, designed to yield simulated tumors as close as possible to the observed ones, vary by an order of magnitude between the three mice analyzed in detail. These differences may reflect morphological and biological variability in tumor growth, as well as errors in the mathematical model, perhaps from an oversimplification of the tumor dynamics or nonidentifiability of parameters. Our results generate parameters that match other experimental in vitro and in vivo measurements. Additionally, we calculate wave speed, which matches with other rat and human measurements.

Key rates for the grades and transformation ability of glioma: model simulations and clinical cases

Tumor progression to higher grade is a fundamental property of cancer. The malignant advancement of the pathological features may either develop during the later stages of cancer growth (natural evolution) or it may necessitate new mutations or molecular events that alter the rates of growth, dispersion, or neovascularization (transformation). Here, we model the pathological and radiological features of grades 2-4 gliomas at the times of diagnosis and death and study grade development and the progression to higher grades. We perform a retrospective review of clinical cases based on model predictions. Simulations uncover two unusual patterns of glioma progression, which are supported by clinical cases: (1) some grades 2 and 3 gliomas lack the ability of progression to higher grades, and (2) grade 3 glioma may evolve to GBM in a few weeks. All 13 gliomas that recurred at the same grade carry either the IDH1-R132H or the ATRX mutation. All (five of five) grade 3 tumors are 1p/19q co-deleted, IDH1-R132H mutated and ATRX wt. Furthermore, three of seven grade 2 gliomas are both IDH1-R132H mutated and ATRX mutated. Simulations replicate the good prognosis of secondary GBM. The results support the hypothesis that constant rates of dispersion, proliferation, and angiogenesis prescribe either a natural evolution or the inability to progress to higher grades. Furthermore, the accrual of molecular events that change a tumor's ability to infiltrate, proliferate or neovascularize may transform the glioma either into a more aggressive tumor at the same grade or elevate its grade.

The role of miR-451 in the switching between proliferation and migration in malignant glioma cells: AMPK signaling, mTOR modulation and Rac1 activation required

Glioblastoma multiforme (GBM), WHO grade IV astrocytoma, is the most common primary neoplasm of the central nervous system (CNS) and has the highest malignancy and mortality rates. The invasive nature of GBM complicates surgical resection and restricts chemotherapeutic access, contributing to poor patient prognosis. The migration of tumor cells is closely related to the tumor cell proliferation. The acquisition of migratory capability, in addition to intracellular factors, is proposed to be a crucial mechanism during the progression of invasion. Using qRT-PCR analysis, we determined that the expression of miR-451 in glioma tissue was lower than in control brain tissue, especially in the central portions of the tumor. In glioma cell lines, we found that decreased miR-451 expression suppressed tumor cell proliferation but enhanced migration with a concomitant low level of CAB39/AMPK/mTOR pathway activation and high level of Rac1/cofilin pathway activation, respectively. Notably, the effect of miR-451 on cytological behavior and on the activation of mTOR and Rac1 was limited when AMPKα1 expression was knocked-down with a synthetic shRNA. We suggest that the glioma microenvironment results in heterogeneity of miR-451 expression. Our data indicated that miR-451 relays environmental signals by upregulating the activity of AMPK signaling, thereby modulating the activation of mTOR and Rac1/cofilin which, in turn, play key roles in glioma cell proliferation and migration, respectively. Our results highlight the need to consider opposing roles of a therapeutic target which, while suppressing tumor cell proliferation, could also promote cell infiltration.

Glioblastoma on a microfluidic chip: Generating pseudopalisades and enhancing aggressiveness through blood vessel obstruction events

Background

Glioblastoma (GBM) is one of the most lethal tumor types. Hypercellular regions, named pseudopalisades, are characteristic in these tumors and have been hypothesized to be waves of migrating glioblastoma cells. These "waves" of cells are thought to be induced by oxygen and nutrient depletion caused by tumor-induced blood vessel occlusion. Although the universal presence of these structures in GBM tumors suggests that they may play an instrumental role in GBM's spread and invasion, the recreation of these structures in vitro has remained challenging.

Methods

Here we present a new microfluidic model of GBM that mimics the dynamics of pseudopalisade formation. To do this, we embedded U-251 MG cells within a collagen hydrogel in a custom-designed microfluidic device. By controlling the medium flow through lateral microchannels, we can mimic and control blood-vessel obstruction events associated with this disease.

Results

Through the use of this new system, we show that nutrient and oxygen starvation triggers a strong migratory process leading to pseudopalisade generation in vitro. These results validate the hypothesis of pseudopalisade formation and show an excellent agreement with a systems-biology model based on a hypoxia-driven phenomenon.

Conclusions

This paper shows the potential of microfluidic devices as advanced artificial systems capable of modeling in vivo nutrient and oxygen gradients during tumor evolution.

Extracting cellular automaton rules from physical Langevin equation models for single and collective cell migration

Cellular automata (CA) are discrete time, space, and state models which are extensively used for modeling biological phenomena. CA are "on-lattice" models with low computational demands. In particular, lattice-gas cellular automata (LGCA) have been introduced as models of single and collective cell migration. The interaction rule dictates the behavior of a cellular automaton model and is critical to the model's biological relevance. The LGCA model's interaction rule has been typically chosen phenomenologically. In this paper, we introduce a method to obtain lattice-gas cellular automaton interaction rules from physically-motivated "off-lattice" Langevin equation models for migrating cells. In particular, we consider Langevin equations related to single cell movement (movement of cells independent of each other) and collective cell migration (movement influenced by cell-cell interactions). As examples of collective cell migration, two different alignment mechanisms are studied: polar and nematic alignment. Both kinds of alignment have been observed in biological systems such as swarms of amoebae and myxobacteria. Polar alignment causes cells to align their velocities parallel to each other, whereas nematic alignment drives cells to align either parallel or antiparallel to each other. Under appropriate assumptions, we have derived the LGCA transition probability rule from the steady-state distribution of the off-lattice Fokker-Planck equation. Comparing alignment order parameters between the original Langevin model and the derived LGCA for both mechanisms, we found different areas of agreement in the parameter space. Finally, we discuss potential reasons for model disagreement and propose extensions to the CA rule derivation methodology.

Single Cell Mathematical Model Successfully Replicates Key Features of GBM: Go-Or-Grow Is Not Necessary

Glioblastoma (GBM) is a malignant brain tumor that continues to be associated with neurological morbidity and poor survival times. Brain invasion is a fundamental property of malignant glioma cells. The Go-or-Grow (GoG) phenotype proposes that cancer cell motility and proliferation are mutually exclusive. Here, we construct and apply a single glioma cell mathematical model that includes motility and angiogenesis and lacks the GoG phenotype. Simulations replicate key features of GBM including its multilayer structure (i.e.edema, enhancement, and necrosis), its progression patterns associated with bevacizumab treatment, and replicate the survival times of GBM treated or untreated with bevacizumab. These results suggest that the GoG phenotype is not a necessary property for the formation of the multilayer structure, recurrence patterns, and the poor survival times of patients diagnosed with GBM.

Why one-size-fits-all vaso-modulatory interventions fail to control glioma invasion: in silico insights

Gliomas are highly invasive brain tumours characterised by poor prognosis and limited response to therapy. There is an ongoing debate on the therapeutic potential of vaso-modulatory interventions against glioma invasion. Prominent vasculature-targeting therapies involve tumour blood vessel deterioration and normalisation. The former aims at tumour infarction and nutrient deprivation induced by blood vessel occlusion/collapse. In contrast, the therapeutic intention of normalising the abnormal tumour vasculature is to improve the efficacy of conventional treatment modalities. Although these strategies have shown therapeutic potential, it remains unclear why they both often fail to control glioma growth. To shed some light on this issue, we propose a mathematical model based on the migration/proliferation dichotomy of glioma cells in order to investigate why vaso-modulatory interventions have shown limited success in terms of tumour clearance. We found the existence of a critical cell proliferation/diffusion ratio that separates glioma responses to vaso-modulatory interventions into two distinct regimes. While for tumours, belonging to one regime, vascular modulations reduce the front speed and increase the infiltration width, for those in the other regime, the invasion speed increases and infiltration width decreases. We discuss how these in silico findings can be used to guide individualised vaso-modulatory approaches to improve treatment success rates.

Tryptophan hydroxylase 1 and 5-HT7 receptor preferentially expressed in triple-negative breast cancer promote cancer progression through autocrine serotonin signaling

BACKGROUND

Triple-negative breast cancer (TNBC) has a high risk of relapse and there are few chemotherapy options. Although 5-hydroxytryptamine (5-HT, serotonin) signaling pathways have been suggested as potential targets for anti-cancer drug development, the mechanism responsible for the action of 5-HT in TNBC remains unknown.

METHODS

Quantitative real-time polymerase chain reaction (qRT-PCR) and Western blotting were used to measure mRNA and protein levels, respectively. Cell proliferation was measured using CellTiter 96 Aqueous One Solution. siRNA transfection was used to assess involvement of genes in cancer invasion, which were identified by Matrigel transwell invasion assay. Levels of 5-HT and vascular endothelial growth factor (VEGF) were measured using ELISA kits. Chick chorioallantoic membrane (CAM) assay and mouse tumor model were used to investigate the in vivo effects of SB269970, a 5-HT₇ receptor antagonist, and BJ-1113, a novel synthetic compound.

RESULTS

TNBC cell lines (MDA-MB-231, HCC-1395, and Hs578T) expressed higher levels of tryptophan hydroxylase 1 (TPH1) than hormone-responsive breast cancer cell lines (MCF-7 and T47D). In MDA-MB-231 cells, 5-HT promoted invasion and proliferation via 5-HT₇ receptor, and interestingly, the stimulatory effect of 5-HT on MDA-MB-231 cell invasion was stronger than its effect on proliferation. Likewise, downstream signaling pathways of 5-HT₇ differed during invasion and proliferation, that is, Gα-activated cAMP and Gβγ-activated kinase signaling during invasion, and Gβγ-activated PI3K/Akt signaling during proliferation. Also, 5-HT increased the protein expressions of TPH1 and VEGF in MDA-MB-231 cells. These results provide insight of the stimulatory effect of 5-HT on breast cancer progression; 5-HT was found to act more strongly during the first stage of metastasis (during invasion and migration) than during the later proliferative phase after local invasion. Interestingly, these actions of 5-HT were inhibited by BJ-1113, a 6-amino-2,4,5-trimethylpyridin-3-ol analog. BJ-1113 blocked intracellular signaling pathways initiated by 5-HT₇ receptor activation, and exhibited anti-proliferative and anti-invasive activities against MDA-MB-231 cells. Furthermore, the inhibitory effect of BJ-1113 against MDA-MB-231 tumor growth was greater than that of SB269970, a 5-HT₇ receptor antagonist.

CONCLUSIONS

5-HT₇ receptor which mediates 5-HT-induced cancer progression is a potential therapeutic target in TNBC, and BJ-1113 offers a novel scaffold for the development of anti-cancer agents against TNBC.

Time-lapse phenotyping of invasive glioma cells ex vivo reveals subtype-specific movement patterns guided by tumor core signaling

The biology of glioblastoma invasion and its mechanisms are poorly understood. We demonstrate using time-lapse microscopy that grafting of glioblastoma (GBM) tumorspheres into rodent brain slices results in experimental ex vivo tumors with invasive properties that recapitulate the invasion observed after orthotopic transplantation into the rodent brain. The migratory movements and mitotic patterns were clearly modified by signals extrinsic to the invading cells. The cells migrated away from the tumorspheres, and removal of the spheres reduced the directed invasive movement. The cell cultures contained different populations of invasive cells that had distinct morphology and invasive behavior patterns. Grafts of the most invasive GBM culture contained 91±8% cells with an invasive phenotype, characterized by small soma with a distinct leading process. Conversely, the majority of cells in less invasive GBM grafts were phenotypically heterogeneous: only 6.3±4.1% of the cells had the invasive phenotype. Grafts of highly and moderately invasive cultures had different proportions of cells that advanced into the brain slice parenchyma during the observation period: 89.2±2.2% and 23.1±6.8%, respectively. In grafts with moderately invasive properties, most of the cells (76.8±6.8%) invading the surrounding brain tissue returned to the tumor bulk or stopped centrifugal migration. Our data suggest that the invasion of individual GBM tumors can be conditioned by the prevalence of a cell fraction with particular invasive morphology and by signaling between the tumor core and invasive cells. These findings can be important for the development of new therapeutic strategies that target the invasive GBM cells.

Phenotypic Transition as a Survival Strategy of Glioma

Malignant glioma is characterized by rapid proliferation, invasion into surrounding central nervous system tissues, and aberrant vascularization. There is increasing evidence that shows gliomas are more complex than previously thought, as each tumor comprises considerable intratumoral heterogeneity with mixtures of genetically and phenotypically distinct subclones. Heterogeneity within and across tumors is recognized as a critical factor that limits therapeutic progress for malignant glioma. Recent genotyping and expression profiling of gliomas has allowed for the creation of classification schemes that assign tumors to subtypes based on similarity to defined expression signatures. Also, malignant gliomas frequently shift their biological features upon recurrence and progression. The ability of glioma cells to resist adverse conditions such as hypoxia and metabolic stress is necessary for sustained tumor growth and strongly influences tumor behaviors. In general, glioma cells are in one of two phenotypic categories: higher proliferative activity with angiogenesis, or higher migratory activity with attenuated proliferative ability. Further, they switch phenotypic categories depending on the situation. To date, a multidimensional approach has been employed to clarify the mechanisms of phenotypic shift of glioma. Various molecular and signaling pathways are involved in phenotypic shifts of glioma, possibly with crosstalk between them. In this review, we discuss molecular and phenotypic heterogeneity of glioma cells and mechanisms of phenotypic shifts in regard to the glioma proliferation, angiogenesis, and invasion. A better understanding of the molecular mechanisms that underlie phenotypic shifts of glioma may provide new insights into targeted therapeutic strategies.

Tumor Budding: The Name is EMT. Partial EMT

Tumor budding is a histological phenomenon encountered in various cancers, whereby individual malignant cells and/or small clusters of malignant cells are seen in the tumor stroma. Postulated to be mirror epithelial-mesenchymal transition, tumor budding has been associated with poor cancer outcomes. However, the vast heterogeneity in its exact definition, methodology of assessment, and patient stratification need to be resolved before it can be routinely used as a standardized prognostic feature. Here, we discuss the heterogeneity in defining and assessing tumor budding, its clinical significance across multiple cancer types, and its prospective implementation in clinical practice. Next, we review the emerging evidence about partial, rather than complete, epithelial-mesenchymal phenotype at the tumor bud level, and its connection with tumor proliferation, quiescence, and stemness. Finally, based on recent literature, indicating a co-expression of epithelial and mesenchymal markers in many tumor buds, we posit tumor budding to be a manifestation of this hybrid epithelial/mesenchymal phenotype displaying collective cell migration.

A multiscale model for glioma spread including cell-tissue interactions and proliferation

Glioma is a broad class of brain and spinal cord tumors arising from glia cells, which are the main brain cells that can develop into neoplasms. They are highly invasive and lead to irregular tumor margins which are not precisely identifiable by medical imaging, thus rendering a precise enough resection very difficult. The understanding of glioma spread patterns is hence essential for both radiological therapy as well as surgical treatment. In this paper we propose a multiscale model for glioma growth including interactions of the cells with the underlying tissue network, along with proliferative effects. Our current accounting for two subpopulations of cells to accomodate proliferation according to the go-or-grow dichtomoty is an extension of the setting in [16]. As in that paper, we assume that cancer cells use neuronal fiber tracts as invasive pathways. Hence, the individual structure of brain tissue seems to be decisive for the tumor spread. Diffusion tensor imaging (DTI) is able to provide such information, thus opening the way for patient specific modeling of glioma invasion. Starting from a multiscale model involving subcellular (microscopic) and individual (mesoscale) cell dynamics, we perform a parabolic scaling to obtain an approximating reaction-diffusion-transport equation on the macroscale of the tumor cell population. Numerical simulations based on DTI data are carried out in order to assess the performance of our modeling approach.

Edge effects in game-theoretic dynamics of spatially structured tumours

Cancer dynamics are an evolutionary game between cellular phenotypes. A typical assumption in this modelling paradigm is that the probability of a given phenotypic strategy interacting with another depends exclusively on the abundance of those strategies without regard for local neighbourhood structure. We address this limitation by using the Ohtsuki-Nowak transform to introduce spatial structure to the go versus grow game. We show that spatial structure can promote the invasive (go) strategy. By considering the change in neighbourhood size at a static boundary--such as a blood vessel, organ capsule or basement membrane--we show an edge effect that allows a tumour without invasive phenotypes in the bulk to have a polyclonal boundary with invasive cells. We present an example of this promotion of invasive (epithelial-mesenchymal transition-positive) cells in a metastatic colony of prostate adenocarcinoma in bone marrow. Our results caution that pathologic analyses that do not distinguish between cells in the bulk and cells at a static edge of a tumour can underestimate the number of invasive cells. Although we concentrate on applications in mathematical oncology, we expect our approach to extend to other evolutionary game models where interaction neighbourhoods change at fixed system boundaries.

SPOCK1 is upregulated in recurrent glioblastoma and contributes to metastasis and Temozolomide resistance

OBJECTIVES

Glioblastoma multiforme (GBM) is the most aggressive brain tumour type in humans. Its poor prognosis is largely attributed to its invasiveness and high rate of recurrence. Recurring GBM is commonly resistant to chemotherapeutic drugs, making it specially difficult to treat. Recent studies have revealed that matricellular glycoprotein SPOCK1 to be upregulated in several cancer types and to be specifically expressed in invasive GBM, but not in other types of non-invasive brain tumour, which prompted us to study the mechanism of action of SPOCK1 in invasion, recurrence and drug resistance of GBM cells.

MATERIALS AND METHODS

SPOCK1 expression in GBM tissues was evaluated using qPCR, Western blotting and immunohistochemical staining. Cell migration was tested by the wound healing method and cell invasion was assessed using transwell plates with Matrigel coating. Western blotting was performed for E-cadherin, vimentin, N-cadherin, p-Akt and Akt. Cell viability was examined using the MTT assay.

RESULTS

We found that the expression of SPOCK1 was significantly upregulated in recurrent GBM. We also demonstrated that SPOCK1 positively regulated migration, invasion and EMT process of GBM cells. Furthermore, SPOCK1 mediated TMZ resistance in GBM, as knockdown of SPOCK1 expression in TMZ-resistant GBM cells substantially sensitized these cells to TMZ.

CONCLUSION

SPOCK1 results were positive and it mediated TMZ resistance in GBM. In addition, SPOCK1 regulated invasion and TMZ resistance in GBM cells via the Akt signalling pathway.

An Arresting Story about Basement Membrane Invasion

In this issue of Developmental Cell, Matus et al. (2015) reveal that to invade past basement membrane, the C. elegans anchor cell must cease dividing before differentiating and expressing pro-invasion genes. This demonstration of invasion and proliferation as mutually incompatible cell states has implications for our understanding of cancer metastasis.

The mathematics of cancer: integrating quantitative models

Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.

The motility-proliferation-metabolism interplay during metastatic invasion

Metastasis is the major cause for cancer patients' death, and despite all the recent advances in cancer research it is still mostly incurable. Understanding the mechanisms that are involved in the migration of the cells in a complex environment is a key step towards successful anti-metastatic treatment. Using experimental data-based modeling, we focus on the fundamentals of metastatic invasion: motility, invasion, proliferation and metabolism, and study how they may be combined to maximize the cancer's ability to metastasize. The modeled cells' performance is measured by the number of cells that succeed in migration in a maze, which mimics the extracellular environment. We show that co-existence of different cell clones in the tumor, as often found in experiments, optimizes the invasive ability in a frequently-changing environment. We study the role of metabolism and stimulation by growth factors, and show that metabolism plays a crucial role in the metastatic process and should therefore be targeted for successful treatment.

An Emerging Allee Effect Is Critical for Tumor Initiation and Persistence

Tumor cells develop different strategies to cope with changing microenvironmental conditions. A prominent example is the adaptive phenotypic switching between cell migration and proliferation. While it has been shown that the migration-proliferation plasticity influences tumor spread, it remains unclear how this particular phenotypic plasticity affects overall tumor growth, in particular initiation and persistence. To address this problem, we formulate and study a mathematical model of spatio-temporal tumor dynamics which incorporates the microenvironmental influence through a local cell density dependence. Our analysis reveals that two dynamic regimes can be distinguished. If cell motility is allowed to increase with local cell density, any tumor cell population will persist in time, irrespective of its initial size. On the contrary, if cell motility is assumed to decrease with respect to local cell density, any tumor population below a certain size threshold will eventually extinguish, a fact usually termed as Allee effect in ecology. These results suggest that strategies aimed at modulating migration are worth to be explored as alternatives to those mainly focused at keeping tumor proliferation under control.

Controlling tumor growth remains a major medical challenge. Current clinical therapies focus on strategies to reduce tumor cell proliferation. However, during tumor progression, tumor cells may switch between proliferative and migratory behaviors, thereby allowing adaptation to microenvironmental changes that result in variations in local tumor cell density. We herein explore by means of a mathematical model the impact of migration-proliferation plasticity on tumor initiation and persistence. Our work suggests that small tumors can become extinct solely by their intrinsic cell population dynamics if cell motility decreases along with local cell density. In contrast, if cell motility increases with cell density, the tumor inevitably grows. Our model suggests that the regulation of cell migration plays a key role in tumor growth as a whole, making this feature a potential target for clinical studies.

The TWEAK receptor Fn14 is a potential cell surface portal for targeted delivery of glioblastoma therapeutics

Fibroblast growth factor-inducible 14 (Fn14; TNFRSF12A) is the cell surface receptor for the tumor necrosis factor (TNF) family member TNF-like weak inducer of apoptosis (TWEAK). The Fn14 gene is normally expressed at low levels in healthy tissues but expression is significantly increased after tissue injury and in many solid tumor types, including glioblastoma (GB; formerly referred to as 'GB multiforme'). GB is the most common and aggressive primary malignant brain tumor and the current standard-of-care therapeutic regimen has a relatively small impact on patient survival, primarily because glioma cells have an inherent propensity to invade into normal brain parenchyma, which invariably leads to tumor recurrence and patient death. Despite major, concerted efforts to find new treatments, a new GB therapeutic that improves survival has not been introduced since 2005. In this review article, we summarize studies indicating that (i) Fn14 gene expression is low in normal brain tissue but is upregulated in advanced brain cancers and, in particular, in GB tumors exhibiting the mesenchymal molecular subtype; (ii) Fn14 expression can be detected in glioma cells residing in both the tumor core and invasive rim regions, with the maximal levels found in the invading glioma cells located within normal brain tissue; and (iii)

TWEAK

Fn14 engagement as well as Fn14 overexpression can stimulate glioma cell migration, invasion and resistance to chemotherapeutic agents in vitro. We also discuss two new therapeutic platforms that are currently in development that leverage Fn14 overexpression in GB tumors as a way to deliver cytotoxic agents to the glioma cells remaining after surgical resection while sparing normal healthy brain cells.

Mathematically modeling the biological properties of gliomas: A review

Although mathematical modeling is a mainstay for industrial and many scientific studies, such approaches have found little application in neurosurgery. However, the fusion of biological studies and applied mathematics is rapidly changing this environment, especially for cancer research. This review focuses on the exciting potential for mathematical models to provide new avenues for studying the growth of gliomas to practical use. In vitro studies are often used to simulate the effects of specific model parameters that would be difficult in a larger-scale model. With regard to glioma invasive properties, metabolic and vascular attributes can be modeled to gain insight into the infiltrative mechanisms that are attributable to the tumor's aggressive behavior. Morphologically, gliomas show different characteristics that may allow their growth stage and invasive properties to be predicted, and models continue to offer insight about how these attributes are manifested visually. Recent studies have attempted to predict the efficacy of certain treatment modalities and exactly how they should be administered relative to each other. Imaging is also a crucial component in simulating clinically relevant tumors and their influence on the surrounding anatomical structures in the brain.

Analysis of individual cell trajectories in lattice-gas cellular automaton models for migrating cell populations

Collective dynamics of migrating cell populations drive key processes in tissue formation and maintenance under normal and diseased conditions. Collective cell behavior at the tissue level is typically characterized by considering cell density patterns such as clusters and moving cell fronts. However, there are also important observables of collective dynamics related to individual cell behavior. In particular, individual cell trajectories are footprints of emergent behavior in populations of migrating cells. Lattice-gas cellular automata (LGCA) have proven successful to model and analyze collective behavior arising from interactions of migrating cells. There are well-established methods to analyze cell density patterns in LGCA models. Although LGCA dynamics are defined by cell-based rules, individual cells are not distinguished. Therefore, individual cell trajectories cannot be analyzed in LGCA so far. Here, we extend the classical LGCA framework to allow labeling and tracking of individual cells. We consider cell number conserving LGCA models of migrating cell populations where cell interactions are regulated by local cell density and derive stochastic differential equations approximating individual cell trajectories in LGCA. This result allows the prediction of complex individual cell trajectories emerging in LGCA models and is a basis for model-experiment comparisons at the individual cell level.

ZEB1 Promotes Invasion in Human Fetal Neural Stem Cells and Hypoxic Glioma Neurospheres

Diffuse spread through brain parenchyma and the presence of hypoxic foci rimmed by neoplastic cells are two cardinal features of glioblastoma, and low oxygen is thought to drive movement of malignant gliomas in the core of the lesions. Transcription factors associated with epithelial-to-mesenchymal transition (EMT) have been linked to this invasion, and we found that hypoxia increased in vitro invasion up to fourfold in glioblastoma neurosphere lines and induced the expression of ZEB1. Immunohistochemical assessment of 295 surgical specimens consisting of various types of pediatric and adult brain cancers showed that ZEB1 expression was significantly higher in infiltrative lesions than less invasive tumors such as pilocytic astrocytoma and ependymoma. ZEB1 protein was also present in human fetal periventricular stem and progenitor cells and ZEB1 inhibition impaired migration of in vitro propagated human neural stem cells. The induction of ZEB1 protein in hypoxic glioblastoma neurospheres could be partially blocked by the HIF1alpha inhibitor digoxin. Targeting ZEB1 blocked hypoxia-augmented invasion of glioblastoma cells in addition to slowing them in normoxia. These data support the role for ZEB1 in invasive and high-grade brain tumors and suggest its key role in promoting invasion in the hypoxic tumor core as well as in the periphery.

Joint fitting reveals hidden interactions in tumor growth

Tumor growth is often the result of the simultaneous development of two or more cancer cell populations. Crucial to the system evolution are the interactions between these populations. To obtain information about these interactions we apply the recently developed vector universality (VUN) formalism to various instances of competition between tumor populations. The formalism allows us (a) to quantify the growth mechanisms of a HeLa cell colony, describing the phenotype switching responsible for its fast expansion, (b) to reliably reconstruct the evolution of the necrotic and viable fractions in both in vitro and in vivo tumors using data for the time dependences of the total masses alone, and (c) to show how the shedding of cells leading to subspheroid formation is beneficial to both the spheroid and subspheroid populations, suggesting that shedding is a strong positive influence on cancer dissemination.

Effects of anti-angiogenesis on glioblastoma growth and migration: model to clinical predictions

Glioblastoma multiforme (GBM) causes significant neurological morbidity and short survival times. Brain invasion by GBM is associated with poor prognosis. Recent clinical trials of bevacizumab in newly-diagnosed GBM found no beneficial effects on overall survival times; however, the baseline health-related quality of life and performance status were maintained longer in the bevacizumab group and the glucocorticoid requirement was lower. Here, we construct a clinical-scale model of GBM whose predictions uncover a new pattern of recurrence in 11/70 bevacizumab-treated patients. The findings support an exception to the Folkman hypothesis: GBM grows in the absence of angiogenesis by a cycle of proliferation and brain invasion that expands necrosis. Furthermore, necrosis is positively correlated with brain invasion in 26 newly-diagnosed GBM. The unintuitive results explain the unusual clinical effects of bevacizumab and suggest new hypotheses on the dynamic clinical effects of migration by active transport, a mechanism of hypoxia-driven brain invasion.

A multilayer grow-or-go model for GBM: effects of invasive cells and anti-angiogenesis on growth

The recent use of anti-angiogenesis (AA) drugs for the treatment of glioblastoma multiforme (GBM) has uncovered unusual tumor responses. Here, we derive a new mathematical model that takes into account the ability of proliferative cells to become invasive under hypoxic conditions; model simulations generate the multilayer structure of GBM, namely proliferation, brain invasion, and necrosis. The model is able to replicate and justify the clinical observation of rebound growth when AA therapy is discontinued in some patients. The model is interrogated to derive fundamental insights int cancer biology and on the clinical and biological effects of AA drugs. Invasive cells promote tumor growth, which in the long run exceeds the effects of angiogenesis alone. Furthermore, AA drugs increase the fraction of invasive cells in the tumor, which explain progression by fluid-attenuated inversion recovery (FLAIR) signal and the rebound tumor growth when AA is discontinued.

Spatial and temporal dynamics of cell generations within an invasion wave: a link to cell lineage tracing

Mathematical models of a cell invasion wave have included both continuum partial differential equation (PDE) approaches and discrete agent-based cellular automata (CA) approaches. Here we are interested in modelling the spatial and temporal dynamics of the number of divisions (generation number) that cells have undergone by any time point within an invasion wave. In the CA framework this is performed from agent lineage tracings, while in the PDE approach a multi-species generalized Fisher equation is derived for the cell density within each generation. Both paradigms exhibit qualitatively similar cell generation densities that are spatially organized, with agents of low generation number rapidly attaining a steady state (with average generation number increasing linearly with distance) behind the moving wave and with evolving high generation number at the wavefront. This regularity in the generation spatial distributions is in contrast to the highly stochastic nature of the underlying lineage dynamics of the population. In addition, we construct a method for determining the lineage tracings of all agents without labelling and tracking the agents, but through either a knowledge of the spatial distribution of the generations or the number of agents in each generation. This involves determining generation-dependent proliferation probabilities and using these to define a generation-dependent Galton-Watson (GDGW) process. Monte-Carlo simulations of the GDGW process are used to determine the individual lineage tracings. The lineages of the GDGW process are analyzed using Lorenz curves and found to be similar to outcomes generated by direct lineage tracing in CA realizations. This analysis provides the basis for a potentially useful technique for deducing cell lineage data when imaging every cell is not feasible.

Exploring the competition between proliferative and invasive cancer phenotypes in a continuous spatial model

Tumor is characterized by extensive heterogeneity with respect to its microenvironment and its genetic composition. We extend a previously developed monoclonal continuous spatial model of tumor growth to account for polyclonal cell populations and investigate the interplay between a more proliferative and a more invasive phenotype under different conditions. The model simulations demonstrate a transition from the dominance of the proliferative to the dominance of the invasive phenotype resembling malignant tumor progression and show a time period where both subpopulations are abundant. As the dominant phenotype switches from proliferative to invasive, the geometry of tumor changes from a compact and almost spherical shape to a more diffusive and fingered morphology with the proliferative phenotype to be restricted in the tumor bulk and the invasive to dominate at tumor edges. Different micro-environmental conditions and different phenotypic properties can promote or inhibit invasion demonstrating their mutual importance. The model provides a computational framework to investigate tumor heterogeneity and the constant interplay between the environment and the specific characteristics of phenotypes that should be taken into account for the prediction of tumor evolution, morphology and effective treatment.

Choindroitinase ABC I-mediated enhancement of oncolytic virus spread and anti tumor efficacy: a mathematical model

Oncolytic viruses are genetically engineered viruses that are designed to kill cancer cells while doing minimal damage to normal healthy tissue. After being injected into a tumor, they infect cancer cells, multiply inside them, and when a cancer cell is killed they move on to spread and infect other cancer cells. Chondroitinase ABC (Chase-ABC) is a bacterial enzyme that can remove a major glioma ECM component, chondroitin sulfate glycosoamino glycans from proteoglycans without any deleterious effects in vivo. It has been shown that Chase-ABC treatment is able to promote the spread of the viruses, increasing the efficacy of the viral treatment. In this paper we develop a mathematical model to investigate the effect of the Chase-ABC on the treatment of glioma by oncolytic viruses (OV). We show that the model's predictions agree with experimental results for a spherical glioma. We then use the model to test various treatment options in the heterogeneous microenvironment of the brain. The model predicts that separate injections of OV, one into the center of the tumor and another outside the tumor will result in better outcome than if the total injection is outside the tumor. In particular, the injection of the ECM-degrading enzyme (Chase-ABC) on the periphery of the main tumor core need to be administered in an optimal strategy in order to infect and eradicate the infiltrating glioma cells outside the tumor core in addition to proliferative cells in the bulk of tumor core. The model also predicts that the size of tumor satellites and distance between the primary tumor and multifocal/satellite lesions may be an important factor for the efficacy of the viral therapy with Chase treatment.

Distinct c-Met activation mechanisms induce cell rounding or invasion through pathways involving integrins, RhoA and HIP1

Many carcinomas have acquired oncogenic mechanisms for activating c-Met, including c-Met overexpression and excessive autocrine or paracrine stimulation with hepatocyte growth factor (HGF). However, the biological outcome of c-Met activation through these distinct modes remains ambiguous. Here, we report that HGF-mediated c-Met stimulation triggers a mesenchymal-type collective cell invasion. By contrast, the overexpression of c-Met promotes cell rounding. Moreover, in a high-throughput siRNA screen that was performed using a library of siRNAs against putative regulators of integrin activity, we identified RhoA and the clathrin-adapter protein HIP1 as crucial c-Met effectors in these morphological changes. Transient RhoA activation was necessary for the HGF-induced invasion, whereas sustained RhoA activity regulated c-Met-induced cell rounding. In addition, c-Met-induced cell rounding correlated with the phosphorylation of filamin A and the downregulation of active cell-surface integrins. By contrast, a HIP1-mediated increase in β1-integrin turnover was required for the invasion triggered by HGF. Taken together, our results indicate that c-Met induces distinct cell morphology alterations depending on the stimulus that activates c-Met.

Carboxymethylcellulose hydrogels support central nervous system-derived tumor-cell chemotactic migration: Comparison with conventional extracellular matrix macromolecules

The local microenvironment plays an important role in maintaining the dynamics of the extracellular matrix and the cell–extracellular matrix relationship. The extracellular matrix is a complex network of macromolecules with distinct mechanical and biochemical characteristics. Disruptions in extracellular matrix homeostasis are associated with the onset of cancer. The extracellular matrix becomes highly disorganized, and the cell–matrix relationship changes, resulting in altered cell-signaling processes and metastasis. Medulloblastoma is one of the most common malignant pediatric brain tumors in the United States. In order to gain a better understanding of the interplay between cell–extracellular matrix interactions and cell-migratory responses in tumors, eight different matrix macromolecule formulations were investigated using a medulloblastoma-derived cell line: poly-d-lysine, matrigel, laminin, collagen 1, fibronectin, a 10% blend of laminin–collagen 1, a 20% blend of laminin–collagen 1, and a cellulose-derived hydrogel, carboxymethylcellulose. Over time, the average changes in cell morphology were quantified in 2D and 3D, as was migration in the presence and absence of the chemoattractant, epidermal growth factor. Data revealed that carboxymethylcellulose allowed for a cell–extracellular matrix relationship typically believed to be present in tumors, with cells exhibiting a rounded, amoeboid morphology consistent with chemotactic migration, while the other matrices promoted an elongated cell shape as well as both haptotactic and chemotactic motile processes. Therefore, carboxymethylcellulose hydrogels may serve as effective platforms for investigating central nervous system-derived tumor-cell migration in response to soluble factors.

The effects of cell compressibility, motility and contact inhibition on the growth of tumor cell clusters using the Cellular Potts Model

There are numerous biological examples where genes associated with migratory ability of cells also confer the cells with an increased fitness even though these genes may not have any known effect on the cell mitosis rates. Here, we provide insight into these observations by analyzing the effects of cell migration, compression, and contact inhibition on the growth of tumor cell clusters using the Cellular Potts Model (CPM) in a monolayer geometry. This is a follow-up of a previous study (Thalhauser et al. 2010) in which a Moran-type model was used to study the interaction of cell proliferation, migratory potential and death on the emergence of invasive phenotypes. Here, we extend the study to include the effects of cell size and shape. In particular, we investigate the interplay between cell motility and compressibility within the CPM and find that the CPM predicts that increased cell motility leads to smaller cells. This is an artifact in the CPM. An analysis of the CPM reveals an explicit inverse-relationship between the cell stiffness and motility parameters. We use this relationship to compensate for motility-induced changes in cell size in the CPM so that in the corrected CPM, cell size is independent of the cell motility. We find that subject to comparable levels of compression, clusters of motile cells grow faster than clusters of less motile cells, in qualitative agreement with biological observations and our previous study. Increasing compression tends to reduce growth rates. Contact inhibition penalizes clumped cells by halting their growth and gives motile cells an even greater advantage. Finally, our model predicts cell size distributions that are consistent with those observed in clusters of neuroblastoma cells cultured in low and high density conditions.

Active Brownian agents with concentration-dependent chemotactic sensitivity

We study a biologically motivated model of overdamped, autochemotactic Brownian agents with concentration-dependent chemotactic sensitivity. The agents in our model move stochastically and produce a chemical ligand at their current position. The ligand concentration obeys a reaction-diffusion equation and acts as a chemoattractant for the agents, which bias their motion towards higher concentrations of the dynamically altered chemical field. We explore the impact of concentration-dependent response to chemoattractant gradients on large-scale pattern formation, by deriving a coarse-grained macroscopic description of the individual-based model, and compare the conditions for emergence of inhomogeneous solutions for different variants of the chemotactic sensitivity. We focus primarily on the so-called receptor-law sensitivity, which models a nonlinear decrease of chemotactic sensitivity with increasing ligand concentration. Our results reveal qualitative differences between the receptor law, the constant chemotactic response, and the so-called log law, with respect to stability of the homogeneous solution, as well as the emergence of different patterns (labyrinthine structures, clusters, and bubbles) via spinodal decomposition or nucleation. We discuss two limiting cases, where the model can be reduced to the dynamics of single species: (I) the agent density governed by a density-dependent effective diffusion coefficient and (II) the ligand field with an effective bistable, time-dependent reaction rate. In the end, we turn to single clusters of agents, studying domain growth and determining mean characteristics of the stationary inhomogeneous state. Analytical results are confirmed and extended by large-scale GPU simulations of the individual based model.

Clinical instability of breast cancer markers is reflected in long-term in vitro estrogen deprivation studies

BACKGROUND

Long-term estrogen deprivation models are widely employed in an in vitro setting to recapitulate the hormonal milieu of breast cancer patients treated with endocrine therapy. Despite the wealth information we have garnered from these models thus far, a comprehensive time-course analysis of the estrogen (ER), progesterone (PR), and human epidermal growth factor 2 (HER-2/neu) receptors on the gene and protein level, coupled with expression array data is currently lacking. We aimed to address this knowledge gap in order to enhance our understanding of endocrine therapy resistance in breast cancer patients.

METHODS

ER positive MCF7 and BT474 breast cancer cells were grown in estrogen depleted medium for 10 months with the ER negative MDA-MB-231 cell line employed as control. ER, PR and HER-2/neu expression were analysed at defined short and long-term time points by immunocytochemistry (ICC), and quantitative real-time RT-PCR (qRT-PCR). Microarray analysis was performed on representative samples.

RESULTS

MCF7 cells cultured in estrogen depleted medium displayed decreasing expression of ER up to 8 weeks, which was then re-expressed at 10 months. PR was also down-regulated at early time points and remained so for the duration of the study. BT474 cells generally displayed no changes in ER during the first 8 weeks of deprivation, however its expression was significantly decreased at 10 months. PR expression was also down-regulated early in BT474 samples and was absent at later time points. Finally, microarray data revealed that genes and cell processes down-regulated in both cell lines at 6 weeks overlapped with those down-regulated in aromatase inhibitor treated breast cancer patients.

CONCLUSIONS

Our data demonstrate that expression of ER, PR, and cell metabolic/proliferative processes are unstable in response to long-term estrogen deprivation in breast cancer cell lines. These results mirror recent clinical findings and again emphasize the utility of LTED models in translational research.

c-Src and neural Wiskott-Aldrich syndrome protein (N-WASP) promote low oxygen-induced accelerated brain invasion by gliomas

Malignant gliomas remain associated with poor prognosis and high morbidity because of their ability to invade the brain; furthermore, human gliomas exhibit a phenotype of accelerated brain invasion in response to anti-angiogenic drugs. Here, we study 8 human glioblastoma cell lines; U251, U87, D54 and LN229 show accelerated motility in low ambient oxygen. Src inhibition by Dasatinib abrogates this phenotype. Molecular discovery and validation studies evaluate 46 molecules related to motility or the src pathway in U251 cells. Demanding that the molecular changes induced by low ambient oxygen are reversed by Dasatinib in U251 cells, identifies neural Wiskott-Aldrich syndrome protein (NWASP), Focal adhesion Kinase (FAK), -Catenin, and Cofilin. However, only Src-mediated NWASP phosphorylation distinguishes the four cell lines that exhibit enhanced motility in low ambient oxygen. Downregulating c-Src or NWASP by RNA interference abrogates the low-oxygen-induced enhancement in motility by in vitro assays and in organotypic brain slice cultures. The findings support the idea that c-Src and NWASP play key roles in mediating the molecular pathogenesis of low oxygen-induced accelerated brain invasion by gliomas.

Pre-irradiation of mouse mammary gland stimulates cancer cell migration and development of lung metastases

Background:

In most patients with breast cancer, radiotherapy induces inflammation that is characterised by an increase of promigratory factors in healthy tissues surrounding the tumour. However, their role in the emergence of the migration phenotype and formation of metastases is still unclear.

Methods:

A single mammary gland of BALB/c mice was irradiated with four doses of 6 Gy given at a 24-h interval. After the last session of irradiation, treated and control mammary glands were either collected for quantification of promigratory and proinflammatory factors or were implanted with fluorescent ubiquitination-based cell cycle indicator (FUCCI)-expressing mouse mammary cancer D2A1 cells. The migration of cancer cells in the mammary glands was monitored by optical imaging. On day 21, mammary tumours and lungs were collected for histology analyses and the quantification of metastases.

Results:

Pre-irradiation of the mammary gland increased by 1.8-fold the migration of cancer cells, by 2-fold the quantity of circulating cancer cells and by 2.4-fold the number of lung metastases. These adverse effects were associated with the induction of interleukin-6 (IL-6) and cyclooxygenase-2 (COX-2).

Conclusion:

The emergence of the metastasis phenotype is believed to be associated with the accumulation of mutations in cancer cells. Our results suggest an alternative mechanism based on promigratory factors from irradiated mammary glands. In clinic, the efficiency of radiotherapy could be improved by anti-inflammatory agents that would prevent the stimulation of cancer cell migration induced by radiation.

Cell migration or cytokinesis and proliferation?--revisiting the "go or grow" hypothesis in cancer cells in vitro

The mortality of patients with solid tumors is mostly due to metastasis that relies on the interplay between migration and proliferation. The "go or grow" hypothesis postulates that migration and proliferation spatiotemporally excludes each other. We evaluated this hypothesis on 35 cell lines (12 mesothelioma, 13 melanoma and 10 lung cancer) on both the individual cell and population levels. Following three-day-long videomicroscopy, migration, proliferation and cytokinesis-length were quantified. We found a significantly higher migration in mesothelioma cells compared to melanoma and lung cancer while tumor types did not differ in mean proliferation or duration of cytokinesis. Strikingly, we found in melanoma and lung cancer a significant positive correlation between mean proliferation and migration. Furthermore, non-dividing melanoma and lung cancer cells displayed slower migration. In contrast, in mesothelioma there were no such correlations. Interestingly, negative correlation was found between cytokinesis-length and migration in melanoma. FAK activation was higher in melanoma cells with high motility. We demonstrate that the cancer cells studied do not defer proliferation for migration. Of note, tumor cells from various organ systems may differently regulate migration and proliferation. Furthermore, our data is in line with the observation of pathologists that highly proliferative tumors are often highly invasive.

Reciprocal activation of transcription factors underlies the dichotomy between proliferation and invasion of glioma cells

Histology of malignant glioma depicts dense proliferative areas rich in angiogenesis as well as dissemination of neoplastic cells into adjacent brain tissue. Although the mechanisms that trigger transition from proliferative to invasive phenotypes are complex, the dichotomy of cell proliferation and migration, the “Go or Grow” hypothesis, argues for specific and coordinated regulation of these phenotypes. We investigated transcriptional elements that accompany the phenotypes of migration and proliferation, and consider the therapeutic significance of the “Go or Grow” hypothesis. Interrogation of matched core and rim regions from human glioblastoma biopsy specimens in situ (n = 44) revealed higher proliferation (Ki67 labeling index) in cells residing at the core compared to the rim. Profiling activated transcription factors in a panel of migration-activated versus migration-restricted GBM cells portrayed strong NF-κB activity in the migratory cell population. In contrast, increased c-Myc activity was found in migration-restricted proliferative cells. Validation of transcriptional activity by NF-κB- or c-Myc-driven GFP or RFP, respectively, showed an increased NF-κB activity in the active migrating cells, whereas the proliferative, migration restricted cells displayed increased c-Myc activity. Immunohistochemistry on clinical specimens validated a robust phosphorylated c-Myc staining in tumor cells at the core, whereas increased phosphorylated NF-κB staining was detected in the invasive tumor cells at the rim. Functional genomics revealed that depletion of c-Myc expression by siRNA oligonucleotides reduced cell proliferation in vitro, but surprisingly, cell migration was enhanced significantly. Conversely, inhibition of NF-κB by pharmacological inhibitors, SN50 or BAY-11, decreased both cell migration in vitro and invasion ex vivo. Notably, inhibition of NF-κB was found to have no effect on the proliferation rate of glioma cells. These findings suggest that the reciprocal and coordinated suppression/activation of transcription factors, such as c-Myc and NF-κB may underlie the shift of glioma cells from a “growing-to-going” phenotype.

Ionizing radiation, ion transports, and radioresistance of cancer cells

The standard treatment of many tumor entities comprises fractionated radiation therapy which applies ionizing radiation to the tumor-bearing target volume. Ionizing radiation causes double-strand breaks in the DNA backbone that result in cell death if the number of DNA double-strand breaks exceeds the DNA repair capacity of the tumor cell. Ionizing radiation reportedly does not only act on the DNA in the nucleus but also on the plasma membrane. In particular, ionizing radiation-induced modifications of ion channels and transporters have been reported. Importantly, these altered transports seem to contribute to the survival of the irradiated tumor cells. The present review article summarizes our current knowledge on the underlying mechanisms and introduces strategies to radiosensitize tumor cells by targeting plasma membrane ion transports.

From patient-specific mathematical neuro-oncology to precision medicine

Gliomas are notoriously aggressive, malignant brain tumors that have variable response to treatment. These patients often have poor prognosis, informed primarily by histopathology. Mathematical neuro-oncology (MNO) is a young and burgeoning field that leverages mathematical models to predict and quantify response to therapies. These mathematical models can form the basis of modern “precision medicine” approaches to tailor therapy in a patient-specific manner. Patient-specific models (PSMs) can be used to overcome imaging limitations, improve prognostic predictions, stratify patients, and assess treatment response in silico. The information gleaned from such models can aid in the construction and efficacy of clinical trials and treatment protocols, accelerating the pace of clinical research in the war on cancer. This review focuses on the growing translation of PSM to clinical neuro-oncology. It will also provide a forward-looking view on a new era of patient-specific MNO.

Regulation of cell proliferation and migration in glioblastoma: new therapeutic approach

Glioblastoma is the most aggressive brain cancer with the poor survival rate. A microRNA, miR-451, and its downstream molecules, CAB39/LKB1/STRAD/AMPK, are known to play a critical role in regulating a biochemical balance between rapid proliferation and invasion in the presence of metabolic stress in microenvironment. We develop a novel multi-scale mathematical model where cell migration and proliferation are controlled through a core intracellular control system (miR-451-AMPK complex) in response to glucose availability and physical constraints in the microenvironment. Tumor cells are modeled individually and proliferation and migration of those cells are regulated by the intracellular dynamics and reaction-diffusion equations of concentrations of glucose, chemoattractant, extracellular matrix, and MMPs. The model predicts that invasion patterns and rapid growth of tumor cells after conventional surgery depend on biophysical properties of cells, dynamics of the core control system, and microenvironment as well as glucose injection methods. We developed a new type of therapeutic approach: effective injection of chemoattractant to bring invasive cells back to the surgical site after initial surgery, followed by glucose injection at the same location. The model suggests that a good combination of chemoattractant and glucose injection at appropriate time frames may lead to an effective therapeutic strategy of eradicating tumor cells.

Hypoxic cell waves around necrotic cores in glioblastoma: a biomathematical model and its therapeutic implications

Glioblastoma is a rapidly evolving high-grade astrocytoma that is distinguished pathologically from lower grade gliomas by the presence of necrosis and microvascular hyperplasia. Necrotic areas are typically surrounded by hypercellular regions known as "pseudopalisades" originated by local tumor vessel occlusions that induce collective cellular migration events. This leads to the formation of waves of tumor cells actively migrating away from central hypoxia. We present a mathematical model that incorporates the interplay among two tumor cell phenotypes, a necrotic core and the oxygen distribution. Our simulations reveal the formation of a traveling wave of tumor cells that reproduces the observed histologic patterns of pseudopalisades. Additional simulations of the model equations show that preventing the collapse of tumor microvessels leads to slower glioma invasion, a fact that might be exploited for therapeutic purposes.

Metabolic associations of reduced proliferation and oxidative stress in advanced breast cancer

Aberrant metabolism is a hallmark of cancer, but whole metabolomic flux measurements remain scarce. To bridge this gap, we developed a novel metabolic phenotypic analysis (MPA) method that infers metabolic phenotypes based on the integration of transcriptomics or proteomics data within a human genome-scale metabolic model. MPA was applied to conduct the first genome-scale study of breast cancer metabolism based on the gene expression of a large cohort of clinical samples. The modeling correctly predicted cell lines' growth rates, tumor lipid levels, and amino acid biomarkers, outperforming extant metabolic modeling methods. Experimental validation was obtained in vitro. The analysis revealed a subtype-independent "go or grow" dichotomy in breast cancer, where proliferation rates decrease as tumors evolve metastatic capability. MPA also identified a stoichiometric tradeoff that links the observed reduction in proliferation rates to the growing need to detoxify reactive oxygen species. Finally, a fundamental stoichiometric tradeoff between serine and glutamine metabolism was found, presenting a novel hallmark of estrogen receptor (ER)(+) versus ER(-) tumor metabolism. Together, our findings greatly extend insights into core metabolic aberrations and their impact in breast cancer.

The impact of phenotypic switching on glioblastoma growth and invasion

The brain tumour glioblastoma is characterised by diffuse and infiltrative growth into surrounding brain tissue. At the macroscopic level, the progression speed of a glioblastoma tumour is determined by two key factors: the cell proliferation rate and the cell migration speed. At the microscopic level, however, proliferation and migration appear to be mutually exclusive phenotypes, as indicated by recent in vivo imaging data. Here, we develop a mathematical model to analyse how the phenotypic switching between proliferative and migratory states of individual cells affects the macroscopic growth of the tumour. For this, we propose an individual-based stochastic model in which glioblastoma cells are either in a proliferative state, where they are stationary and divide, or in motile state in which they are subject to random motion. From the model we derive a continuum approximation in the form of two coupled reaction-diffusion equations, which exhibit travelling wave solutions whose speed of invasion depends on the model parameters. We propose a simple analytical method to predict progression rate from the cell-specific parameters and demonstrate that optimal glioblastoma growth depends on a non-trivial trade-off between the phenotypic switching rates. By linking cellular properties to an in vivo outcome, the model should be applicable to designing relevant cell screens for glioblastoma and cytometry-based patient prognostics.

In this work, we develop a spatial mathematical model in order to analyse the growth behavior of the brain tumour glioblastoma. Tumours of this type have a diffuse boundary, with considerable local invasion of surrounding brain tissue, making surgery difficult. At the cellular level, the progression of a glioblastoma is known to depend on the balance between cell division (proliferation) and cell movement (migration). Based on recent evidence, our model assumes that each cell in a glioblastoma tumour resides in either of two mutually exclusive states: proliferating or migrating. From a probabilistic model of switching between these two phenotypes, we go on to derive equations that link cellular phenotypes to disease progression. The model has several possible applications. For instance, it could be used to predict the rate of disease progression in an individual patient, and to improve screening methods.

Invasion from a cell aggregate--the roles of active cell motion and mechanical equilibrium

Cell invasion from an aggregate into a surrounding extracellular matrix (ECM) is an important process during development disease, e.g., vascular network assembly or tumor progression. To describe the behavior emerging from autonomous cell motility, cell-cell adhesion and contact guidance by ECM filaments, we propose a suitably modified cellular Potts model. We consider an active cell motility process in which internal polarity is governed by a positive feedback from cell displacements, a mechanism that can result in highly persistent motion when constrained by an oriented ECM structure. The model allows us to explore the interplay between haptotaxis, matrix degradation and active cell movement. We show that for certain conditions the cells are able to both invade the ECM and follow the ECM tracks. Furthermore, we argue that enforcing mechanical equilibrium within a bulk cell mass is of key importance in multicellular simulations.