A quantitative model for differential motility of gliomas in grey and white matter

We have extended a mathematical model of gliomas based on proliferation and diffusion rates to incorporate the effects of augmented cell motility in white matter as compared to grey matter. Using a detailed mapping of the white and grey matter in the brain developed for a MRI simulator, we have been able to simulate model tumours on an anatomically accurate brain domain. Our simulations show good agreement with clinically observed tumour geometries and suggest paths of submicroscopic tumour invasion not detectable on CT or MRI images. We expect this model to give insight into microscopic and submicroscopic invasion of the human brain by glioma cells. This method gives insight in microscopic and submicroscopic invasion of the human brain by glioma cells. Additionally, the model can be useful in defining expected pathways of invasion by glioma cells and thereby identify regions of the brain on which to focus treatments.     

A Computational Model Incorporating Neural Stem Cell Dynamics Reproduces Glioma Incidence across the Lifespan in the Human Population

Glioma is the most common form of primary brain tumor. Demographically, the risk of occurrence increases until old age. Here we present a novel computational model to reproduce the probability of glioma incidence across the lifespan. Previous mathematical models explaining glioma incidence are framed in a rather abstract way, and do not directly relate to empirical findings. To decrease this gap between theory and experimental observations, we incorporate recent data on cellular and molecular factors underlying gliomagenesis. Since evidence implicates the adult neural stem cell as the likely cell-of-origin of glioma, we have incorporated empirically-determined estimates of neural stem cell number, cell division rate, mutation rate and oncogenic potential into our model. We demonstrate that our model yields results which match actual demographic data in the human population. In particular, this model accounts for the observed peak incidence of glioma at approximately 80 years of age, without the need to assert differential susceptibility throughout the population. Overall, our model supports the hypothesis that glioma is caused by randomly-occurring oncogenic mutations within the neural stem cell population. Based on this model, we assess the influence of the (experimentally indicated) decrease in the number of neural stem cells and increase of cell division rate during aging. Our model provides multiple testable predictions, and suggests that different temporal sequences of oncogenic mutations can lead to tumorigenesis. Finally, we conclude that four or five oncogenic mutations are sufficient for the formation of glioma.     

On a Minimal Model for Hemodynamics and Metabolism of Lactate: Application to Low Grade Glioma and Therapeutic Strategies

WHO II low grade glioma evolves inevitably to anaplastic transformation. Magnetic resonance imaging is a good non-invasive way to watch it, by hemodynamic and metabolic modifications, thanks to multinuclear spectroscopy ¹H/³¹P. In this work we study a multi-scale minimal model of hemodynamics and metabolism applied to the study of gliomas. This mathematical analysis leads us to a fast-slow system. The control of the position of the stationary point brings to the concept of domain of viability. Starting from this system, the equations bring to light the parameters that push glioma cells out of their domain of viability. Four fundamental factors are highlighted. The first two are cerebral blood flow and the rate of lactate transport through monocarboxylate transporters, which must be reduced in order to push glioma out of its domain of viability. Another factor is the intra arterial lactate, which must be increased. The last factor is pH, indeed a decrease of intra cellular pH could interfere with glioma growth. These reflections suggest that these four parameters could lead to new therapeutic strategies for the management of low grade gliomas.     

Augmented cell-graphs for automated cancer diagnosis

This work reports a novel computational method based on augmented cell-graphs (ACG), which are constructed from low-magnification tissue images for the mathematical diagnosis of brain cancer (malignant glioma). An ACG is a simple, undirected, weighted and complete graph in which a node represents a cell cluster and an edge between a pair of nodes defines a binary relationship between them. Both the nodes and the edges of an ACG are assigned weights to capture more information about the topology of the tissue. In this work, the experiments are conducted on a dataset that is comprised of 646 human brain biopsy samples from 60 different patients. It is shown that the ACG approach yields sensitivity of 97.53% and specificities of 93.33 and 98.15% (for the inflamed and healthy, respectively) at the tissue level in glioma diagnosis.     

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.     

The probable cell of origin of NF1- and PDGF-driven glioblastomas

Primary glioblastomas are subdivided into several molecular subtypes. There is an ongoing debate over the cell of origin for these tumor types where some suggest a progenitor while others argue for a stem cell origin. Even within the same molecular subgroup, and using lineage tracing in mouse models, different groups have reached different conclusions. We addressed this problem from a combined mathematical modeling and experimental standpoint. We designed a novel mathematical framework to identify the most likely cells of origin of two glioma subtypes. Our mathematical model of the unperturbed in vivo system predicts that if a genetic event contributing to tumor initiation imparts symmetric self-renewing cell division (such as PDGF overexpression), then the cell of origin is a transit amplifier. Otherwise, the initiating mutations arise in stem cells. The mathematical framework was validated with the RCAS/tv-a system of somatic gene transfer in mice. We demonstrated that PDGF-induced gliomas can be derived from GFAP-expressing cells of the subventricular zone or the cortex (reactive astrocytes), thus validating the predictions of our mathematical model. This interdisciplinary approach allowed us to determine the likelihood that individual cell types serve as the cells of origin of gliomas in an unperturbed system.     

A Mathematical Model for the Glucose-Lactate Metabolism of in Vitro Cancer Cells

We propose a mathematical model of tumor cell nutrient uptake governed by the presence of two key biomolecular fuels: glucose and lactate. The model allows us to describe, in a remarkably simple way, different in vitro scenarios previously reported in experiments of tumor cell metabolism using distinct energy sources. The predictions of our model show good agreement with all the examined tumor cell lines (cervix, colon, and glioma) and provide a first step toward the development of more comprehensive frameworks accounting for in vivo cancer dynamics under complex spatial heterogeneities.     

A Mathematical Model to Elucidate Brain Tumor Abrogation by Immunotherapy with T11 Target Structure

T11 Target structure (T11TS), a membrane glycoprotein isolated from sheep erythrocytes, reverses the immune suppressed state of brain tumor induced animals by boosting the functional status of the immune cells. This study aims at aiding in the design of more efficacious brain tumor therapies with T11 target structure. We propose a mathematical model for brain tumor (glioma) and the immune system interactions, which aims in designing efficacious brain tumor therapy. The model encompasses considerations of the interactive dynamics of glioma cells, macrophages, cytotoxic T-lymphocytes (CD8+ T-cells), TGF-β, IFN-γ and the T11TS. The system undergoes sensitivity analysis, that determines which state variables are sensitive to the given parameters and the parameters are estimated from the published data. Computer simulations were used for model verification and validation, which highlight the importance of T11 target structure in brain tumor therapy.     

A mathematical model of glioma growth: the effect of chemotherapy on spatio-temporal growth

During the past two decades computerized tomography (CT) and magnetic resonance imaging (MRI) have permitted the detection of tumours at much earlier stages in their development than was previously possible. In spite of this earlier diagnosis the effects of earlier and more extensive treatments have been difficult to document. This failure has led to an increasing awareness of the importance of infiltration of glioma cells into surrounding grossly normal brain tissue such that recurrence still occurs. In this paper a simple mathematical model for the proliferation and infiltration of such tumours is introduced, based in part on quantitative image analysis of histological sections of a human brain glioma and especially on cross-sectional area/volume measurements of serial CT images while the patient was undergoing chemotherapy. The model parameters were estimated using optimization techniques to give the best fit of the simulated tumour area to the CT scan data. Numerical solution of the model on a two-dimensional domain, which took into account the geometry of the brain and its natural barriers to diffusion, was used to determine the effect of chemotherapy on the spatiotemporal growth of the tumour.     

Improving alloreactive CTL immunotherapy for malignant gliomas using a simulation model of their interactive dynamics

Glioblastoma (GBM), a highly aggressive (WHO grade IV) primary brain tumor, is refractory to traditional treatments, such as surgery, radiation or chemotherapy. This study aims at aiding in the design of more efficacious GBM therapies. We constructed a mathematical model for glioma and the immune system interactions, that may ensue upon direct intra-tumoral administration of ex vivo activated alloreactive cytotoxic-T-lymphocytes (aCTL). Our model encompasses considerations of the interactive dynamics of aCTL, tumor cells, major histocompatibility complex (MHC) class I and MHC class II molecules, as well as cytokines, such as TGF-β and IFN-γ, which dampen or increase the pro-inflammatory environment, respectively. Computer simulations were used for model verification and for retrieving putative treatment scenarios. The mathematical model successfully retrieved clinical trial results of efficacious aCTL immunotherapy for recurrent anaplastic oligodendroglioma and anaplastic astrocytoma (WHO grade III). It predicted that cellular adoptive immunotherapy failed in GBM because the administered dose was 20-fold lower than required for therapeutic efficacy. Model analysis suggests that GBM may be eradicated by new dose-intensive strategies, e.g., 3 × 10⁸ aCTL every 4 days for small tumor burden, or 2 × 10⁹ aCTL, infused every 5 days for larger tumor burden. Further analysis pinpoints crucial bio-markers relating to tumor growth rate, tumor size, and tumor sensitivity to the immune system, whose estimation enables regimen personalization. We propose that adoptive cellular immunotherapy was prematurely abandoned. It may prove efficacious for GBM, if dose intensity is augmented, as prescribed by the mathematical model. Re-initiation of clinical trials, using calculated individualized regimens for grade III–IV malignant glioma, is suggested. An erratum to this article can be found at     

Oleanolic Acid Suppresses Migration and Invasion of Malignant Glioma Cells by Inactivating MAPK/ERK Signaling Pathway

Mitogen-activated protein kinases/Extracellular signal-regulated kinase (MAPK/ERK) pathway is essential for migration and invasion of malignant glioma. It is efficient to inhibit migration and invasion of glioma cells by targeting this pathway. Oleanolic acid (OA) has been well demonstrated to suppress survival, growth and angiogenesis of glioma cells. However, it is still unknown if OA affects the migration and invasion of glioma cells. We utilized U-87 MG glioma cell lines and primary glioma cells from patients to study the effect of OA on migration and invasion of glioma cells with multidisciplinary approaches. In this study, we found that OA significantly decreased the ability of glioma cells to migrate and invade. Epithelial-mesenchymal transition (EMT) of glioma cells was also suppressed by OA treatment. Furthermore, MAPK/ERK pathway was greatly inhibited in glioma cells under OA treatment. MAPK/ERK reactivation induced by a recombinant lentiviral vector, Lv-MEK, was able to rescue the inhibitory effect of OA on migration and invasion of glioma cells. Taken together, we provided evidences that OA was a MAPK/ERK pathway-targeting anti-tumor agent. Although the concentrations we used exceeded its physiological level, OA may be used to prevent migration and invasion of glioma cells by developing its derivatives with enhanced bioactivity.     

In vitro studies on the cell-mediated immune response to human brain tumors. II. Leukocyte-induced coats of glycosaminoglycan increase the resistance of glioma cells to cellular immune attack

We have examined the ability of cultured human glioma cells to elicit allogeneic cytolytic lymphocyte responses in vitro in order to delineate properties of glioma cells that may contribute to their ability to escape cellular immune attack. When glioma cells were cultured together with allogeneic peripheral blood mononuclear cells (PBMC) in mixed lymphocyte-tumor cultures (MLTC), it was observed that cells from eight of 12 glioma lines were surrounded by clear pericellular "halos," which appeared to impede contact between PBMC and the glioma cells. Enzymatic, histochemical, and immunochemical studies indicated that these halos represented glycosaminoglycan (GAG) coats that contained hyaluronic acid (HA) as a major constituent. Electron microscopic studies demonstrated the presence of many thin microvillous processes spanning the width of the halos. The presence of GAG coats around glioma cells in MLTC reduced the generation of cytolytic T lymphocytes specific for antigens on the glioma cells. Likewise, these cell coats decreased the lysis of glioma cells by cytolytic lymphocytes, once generated. The production of thick coats of GAG by glioma cells was induced by interaction of glioma cells with a nondialyzable factor produced by PBMC in culture. This factor did not cause glioma cells to release increased amounts of HA into the medium, but rather increased the production of HA that remained associated with the glioma cell surface. The formation of thick, protective GAG coats by glioma cells as a result of their interaction with the PBMC-derived factor constitutes a nonspecific suppressor mechanism that may contribute to the ability of this class of human solid tumors to evade cellular immune attack.     

A dual functional fluorescent probe for glioma imaging mediated by Blood-brain barrier penetration and glioma cell targeting

Glioma is a huge threat for human being because it was hard to be completely removed owing to both the infiltrating growth of glioma cells and integrity of blood brain barrier. Thus effectively imaging the glioma cells may pave a way for surgical removing of glioma. In this study, a fluorescent probe, Cy3, was anchored onto the terminal of AS1411, a glioma cell targeting aptamer, and then TGN, a BBB targeting peptide, was conjugated with Cy3-AS1411 through a PEG linker. The production, named AsT, was characterized by gel electrophoresis, ¹H NMR and FTIR. In vitro cellular uptake and glioma spheroid uptake demonstrated the AsT could not only be uptaken by both glioma and endothelial cells, but also penetrate through endothelial cell monolayer and uptake by glioma spheroids. In vivo, AsT could effectively target to glioma with high intensity. In conclusion, AsT could be used as an effective glioma imaging probe.     

Glutamate/glutamine metabolism coupling between astrocytes and glioma cells: Neuroprotection and inhibition of glioma growth

Glioma glutamate release has been shown to promote the growth of glioma cells and induce neuronal injuries from epilepsy to neuronal death. However, potential counteractions from normal astrocytes against glioma glutamate release have not been fully evaluated. In this study, we investigated the glutamate/glutamine cycling between glioma cells and astrocytes and their impact on neuronal function. Co-cultures of glioma cells with astrocytes (CGA) in direct contact were established under different mix ratio of astrocyte/glioma. Culture medium conditioned in these CGAs were sampled for HPLC measurement, for neuronal ratiometric calcium imaging, and for neuronal survival assay. We found: (1) High levels of glutaminase expression in glioma cells, but not in astrocytes, glutaminase enables glioma cells to release large amount of glutamate in the presence of glutamine. (2) Glutamate levels in CGAs were directly determined by the astrocyte/glioma ratios, indicating a balance between glioma glutamate release and astrocyte glutamate uptake. (3) Culture media from CGAs of higher glioma/astrocyte ratios induced stronger neuronal Ca²⁺ response and more severe neuronal death. (4) Co-culturing with astrocytes significantly reduced the growth rate of glioma cells. These results indicate that normal astrocytes in the brain play pivotal roles in glioma growth inhibition and in reducing neuronal injuries from glioma glutamate release. However, as tumor growth, the protective role of astrocytes gradually succumb to glioma 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.     

Long noncoding RNA HOXD-AS2 regulates cell cycle to promote glioma progression

Now, numerous exciting findings have been found that long noncoding RNAs (lncRNAs) play a vital role in cancer malignant progression. However, their potential involvement in glioma is not well understood. Here, we performed a high-throughput microarray to detect the lncRNA expression profiles between glioma cell lines and normal astrocyte cell lines. HOXD-AS2 was increased in glioma cells and it was associated with glioma grade and poor prognosis. Loss of HOXD-AS2 can inhibit glioma cell growth by inducing cell-cycle G1 arrest in vitro. The proliferation of glioma was inhibited followed by knocking down the expression of HOXD-AS2 not only in subcutaneous injection model but also in orthotopic implantation model. These findings indicate that HOXD-AS2 promotes the glioma progression and may serve as a potential target for glioma diagnosis and therapy.     

HAX1 maintains the glioma progression in hypoxia through promoting mitochondrial fission

HCLS1-associated protein X-1 (HAX1), an anti-apoptotic molecular, overexpresses in glioma. However, the role of HAX1 in glioma cell surviving in hypoxic environment remains unclear. Western blotting, qRT-PCR, Transwell assay, TUNEL assay, wounding healing assay, clone formation, tumour xenograft model and immunohistochemical staining were used to investigate the role of HAX1 in glioma. HAX1 regulated by HIF-1α was increased in glioma cells cultured in hypoxia. Silencing of HAX1 could cause an increased apoptosis of glioma cells cultured in hypoxia. Silencing of HAX1 also decreased the proliferation, migration and invasion of glioma cells cultured in hypoxia. Increased mitochondrial fission could prevent glioma cells from the damage induced by HAX1 knockdown in hypoxia. Furthermore, HAX1 was found to regulate glioma cells through phosphorylated AKT/Drp signal pathway. In conclusion, our study suggested that HAX1 promoted survival of glioma cells in hypoxic environment via AKT/Drp signal pathway. Our study also provided a potential therapeutic target for glioma.     

miR451 and AMPK mutual antagonism in glioma cell migration and proliferation: a mathematical model

Glioblastoma multiforme (GBM) is the most common and the most aggressive type of brain cancer; the median survival time from the time of diagnosis is approximately one year. GBM is characterized by the hallmarks of rapid proliferation and aggressive invasion. miR-451 is known to play a key role in glioblastoma by modulating the balance of active proliferation and invasion in response to metabolic stress in the microenvironment. The present paper develops a mathematical model of GBM evolution which focuses on the relative balance of growth and invasion. In the present work we represent the miR-451/AMPK pathway by a simple model and show how the effects of glucose on cells need to be "refined" by taking into account the recent history of glucose variations. The simulations show how variations in glucose significantly affect the level of miR-451 and, in turn, cell migration. The model predicts that oscillations in the levels of glucose increase the growth of the primary tumor. The model also suggests that drugs which upregulate miR-451, or block other components of the CAB39/AMPK pathway, will slow down glioma cell migration. The model provides an explanation for the growth-invasion cycling patterns of glioma cells in response to high/low glucose uptake in microenvironment in vitro, and suggests new targets for drugs, associated with miR-451 upregulation.     

Knockdown of DIXDC1 Inhibits the Proliferation and Migration of Human Glioma Cells

DIX domain containing 1 (DIXDC1), the human homolog of coiled-coil-DIX1 (Ccd1), is a positive regulator of Wnt signaling pathway. Recently, it was found to act as a candidate oncogene in colon cancer, non-small-cell lung cancer, and gastric cancer. In this study, we aimed to investigate the clinical significance of DIXDC1 expression in human glioma and its biological function in glioma cells. Western blot and immunohistochemistry analysis showed that DIXDC1 was overexpressed in glioma tissues and glioma cell lines. The expression level of DIXDC1 was evidently linked to glioma pathological grade and Ki-67 expression. Kaplan–Meier curve showed that high expression of DIXDC1 may lead to poor outcome of glioma patients. Serum starvation and refeeding assay indicated that the expression of DIXDC1 was associated with cell cycle. To determine whether DIXDC1 could regulate the proliferation and migration of glioma cells, we transfected glioma cells with interfering RNA-targeting DIXDC1; investigated cell proliferation with Cell Counting Kit (CCK)-8, flow cytometry assays, and colony formation analyses; and investigated cell migration with wound healing assays and transwell assays. According to our data, knockdown of DIXDC1 significantly inhibited proliferation and migration of glioma cells. These data implied that DIXDC1 might participate in the development of glioma, suggesting that DIXDC1 can become a potential therapeutic strategy for glioma.     

miR-484/MAP2/c-Myc-positive regulatory loop in glioma promotes tumor-initiating properties through ERK1/2 signaling

Glioma is the most common intracranial malignant tumor. Cancer stem cells (CSCs) are resistant to chemotherapy and radiotherapy, and are closely related to cancer metastasis and recurrence. In this study, we aimed to explore the effect of miR-484 on glioma stemness and the underlying mechanism involved. miR-484 enhanced glioma tumor-initiating properties in vitro and in vivo. Moreover, miR-484 was shown to directly target MAP2, resulting in activation of ERK1/2 signaling and promotion of stemness in glioma. The ERK1/2 signaling facilitated the formation of a miR-484/MAP2/c-Myc positive feedback loop in glioma. High miR-484 expression predicted a poor prognosis for glioma patients, and high MAP2 expression predicted a good prognosis for glioma patients. Low miR-484 expression and high MAP2 expression was associated with the best prognosis in glioma. Our study suggests that miR-484 and MAP2 can be utilized as predictors for the clinical diagnosis and prognosis of glioma, and miR-484 and MAP2 are potential targets for the treatment of glioma.