Mathematical modelling of tumour-induced angiogenesis

The growth of solid tumours beyond a critical size is dependent upon angiogenesis, the formation of new blood vessels from an existing vasculature. Tumours may remain dormant at microscopic sizes for some years before switching to a mode in which growth of a supportive vasculature is initiated. The new blood vessels supply nutrients, oxygen, and access to routes by which tumour cells may travel to other sites within the host (metastasize). In recent decades an abundance of biological research has focused on tumour-induced angiogenesis in the hope that treatments targeted at the vasculature may result in a stabilisation or regression of the disease: a tantalizing prospect. The complex and fascinating process of angiogenesis has also attracted the interest of researchers in the field of mathematical biology, a discipline that is, for mathematics, relatively new. The challenge in mathematical biology is to produce a model that captures the essential elements and critical dependencies of a biological system. Such a model may ultimately be used as a predictive tool. In this thesis we examine a number of aspects of tumour-induced angiogenesis, focusing on growth of the neovasculature external to the tumour. Firstly we present a one-dimensional continuum model of tumour-induced angiogenesis in which elements of the immune system or other tumour-cytotoxins are delivered via the newly formed vessels. This model, based on observations from experiments by Judah Folkman et al., is able to show regression of the tumour for some parameter regimes. The modelling highlights a number of interesting aspects of the process that may be characterised further in the laboratory. The next model we present examines the initiation positions of blood vessel sprouts on an existing vessel, in a two-dimensional domain. This model hypothesises that a simple feedback inhibition mechanism may be used to describe the spacing of these sprouts with the inhibitor being produced by breakdown of the existing vessel's basement membrane. Finally, we have developed a stochastic model of blood vessel growth and anastomosis in three dimensions. The model has been implemented in C++, includes an openGL interface, and uses a novel algorithm for calculating proximity of the line segments representing a growing vessel. This choice of programming language and graphics interface allows for near-simultaneous calculation and visualisation of blood vessel networks using a contemporary personal computer. In addition the visualised results may be transformed interactively, and drop-down menus facilitate changes in the parameter values. Visualisation of results is of vital importance in the communication of mathematical information to a wide audience, and we aim to incorporate this philosophy in the thesis. As biological research further uncovers the intriguing processes involved in tumourinduced angiogenesis, we conclude with a comment from mathematical biologist Jim Murray, Mathematical biology is : : : the most exciting modern application of mathematics.

An improved model of tumour-immune system interactions

The immune system plays an important role in defending the body against tumours and other threats. Currently, mechanisms involved in immune system interactions with tumour cells are not fully understood. Here we develop a mathematical tool that can be used in aiding to address this shortfall in understanding. This paper de- scribes a hybrid cellular automata model of the interaction between a growing tumour and cells of the innate and specific immune system including the effects of chemokines that builds on previous models of tumour-immune system interactions. In particular, the model is focused on the response of immune cells to tumour cells and how the dynamics of the tumour cells change due to the immune system of the host. We present results and predictions of in silico experiments including simulations of Kaplan-Meier survival-like curves.

Heparan sulfate proteoglycans, tumour progression and the cancer stem cell niche

The cancer stem cell hypothesis states that tumours arise from cells with the ability to self-renew and differentiate into multiple cell types, and that these cells persist in tumors as a distinct population that can cause disease relapse and hence metastasis. The crux of this hypothesis is that these cells are the only cells capable of, by themselves, giving rise to new tumours. What proportion of a tumour consists of these stem cells, where are they localised, how are they regulated, and how can we identify them? The stromal cells embedded within the extracellular matrix (ECM) not only provide a scaffold but also produce ECM constituents for use by stem cells. Heparan sulfate proteoglycans (HSPGs) are ubiquitous to this cell niche and interact with a large number of ligands including growth factors, their receptors, and ECM structural components. It is still unclear whether ECM degradation and subsequent metastasis is a result of proteases produced by the tumour cells themselves or by cells within the stromal compartment. The identification of the cellular origin of cancer stem cells along with microenvironmental changes involved in the initiation, progression and the malignant conversion of all cancers is critical to the development of targeted therapeutics. As ubiquitous members of the ECM microenvironment and hence the cancer cell niche, HSPGs are candidates for a central role in these processes.

Cancer : the to and fro of tumour spread

The spread of cells from the primary site of a solid tumour to distant sites remains the major cause of disease and death associated with these cancers. For tumour cells to spread, or metastasize, they must modify their 'anchored' state and detach from their neighbouring cells; migrate through tissues into the blood and lymph systems; survive in these circulation systems; and then leave the vessels at an appropriate site to form another tumour1. Many of these events are favoured by conversions between two cellular states — the epithelial and mesenchymal phenotypes. But the role of these transitions in cancer metastasis is controversial. Writing in Cancer Cell, Tsai et al.2 and Ocaña et al.3 help to clarify this issue...

Breast cancer stem cells and epithelial mesenchymal plasticity : implications for chemoresistance

Tumour heterogeneity is a key characteristic of cancer and has significant implications relating to tumour response to chemotherapy as well as patient prognosis and potential relapse. It is being increasingly accepted that tumours are clonal in origin, suggestive of a tumour arising from a deregulated or mutated cell. Cancer stem cells (CSC) possess these capabilities, and with appropriate intracellular triggers and/or signalling from extracellular environments, can purportedly differentiate to initiate tumour formation. Additionally through epithelial mesenchymal plasticity (EMP), where cells gain and maintain characteristics of both epithelial and mesenchymal cell types, epithelial-derived tumour cells have been shown to de-differentiate to acquire cancer stem attributes, which also impart chemotherapy resistance. This new paradigm places EMP centrally in the process of tumour progression and metastasis, as well as modulating drug response to current forms of chemotherapy. Furthermore, EMP and CSCs have been identified in cancers arising from different tissue types making it a possible generic therapeutic target in cancer biology. Using breast cancer (BrCa) as an example, we summarise here the current understanding of CSCs, the role of EMP in cancer biology - especially in CSCs and different molecular subtypes, and the implications this has for current and future cancer treatment strategies.

Mechanisms of tumour invasion and metastasis : emerging targets for therapy

The progression of a tumour from one of benign and delimited growth to one that is invasive and metastatic is the major cause of poor clinical outcome in cancer patients. The invasion and metastasis of tumours is a highly complex and multistep process that requires a tumour cell to modulate its ability to adhere, degrade the surrounding extracellular matrix, migrate, proliferate at a secondary site and stimulate angiogenesis. Knowledge of the process has greatly increased and this has resulted in the identification of a number of molecules that are fundamental to the process. The involvement of these molecules has been shown to relate not only to the survival and proliferation of the tumour cell but, also to the processes of tumour cell adhesion, migration, and the tumour cells ability to degrade and escape the primary site as well as play a role in angiogenesis. These molecules may provide important therapeutic targets that represent the ability to target specific steps in the process of invasion and metastasis and provide additional therapies. The review focuses on representative key targets in each of these processes and summarises the state of play in each case.

Mitochondrial genome acquisition restores respiratory function and tumorigenic potential of cancer cells without mitochondrial DNA

We report that tumor cells devoid of their mitochondrial genome (mtDNA) show delayed tumor growth and that tumor formation is associated with acquisition of mtDNA from host cells. This leads to partial recovery of mitochondrial function in cells derived from primary tumors grown from cells without mtDNA and a shorter lag in tumor growth. Cell lines from circulating tumor cells showed further recovery of mitochondrial respiration and an intermediate lag to tumor growth, while cells from lung metastases exhibited full restoration of respiratory function and no lag in tumor growth. Stepwise assembly of mitochondrial respiratory supercomplexes was correlated with acquisition of respiratory function. Our findings indicate horizontal transfer of mtDNA from host cells in the tumor microenvironment to tumor cells with compromised respiratory function to re-establish respiration and tumor-initiating efficacy. These results suggest a novel pathophysiological process for overcoming mtDNA damage and support the notion of high plasticity of malignant cells.

A hybrid cellular automata model of multicellular tumour spheroid growth in hypoxic microenvironment

A three-dimensional hybrid cellular automata (CA) model is developed to study the dynamic process of multicellular tumour spheroid (MTS) growth by introducing hypoxia as an important microenvironment factor which influences cell migration and cell phenotype expression. The model enables us to examine the effects of different hypoxic environments on the growth history of the MTS and to study the dynamic interactions between MTS growth and chemical environments. The results include the spatial distribution of different phenotypes of tumour cells and associated oxygen concentration distributions under hypoxic conditions. The discussion of the model system responses to the varied hypoxic conditions reveals that the improvement of the resistance of tumour cells to a hypoxic environment may be important in the tumour normalization therapy.

3D numerical simulation of avascular tumour growth: effect of hypoxic micro-environment in host tissue

A three-dimensional (3D) mathematical model of tumour growth at the avascular phase and vessel remodelling in host tissues is proposed with emphasis on the study of the interactions of tumour growth and hypoxic micro-environment in host tissues. The hybrid based model includes the continuum part, such as the distributions of oxygen and vascular endothelial growth factors (VEGFs), and the discrete part of tumour cells (TCs) and blood vessel networks. The simulation shows the dynamic process of avascular tumour growth from a few initial cells to an equilibrium state with varied vessel networks. After a phase of rapidly increasing numbers of the TCs, more and more host vessels collapse due to the stress caused by the growing tumour. In addition, the consumption of oxygen expands with the enlarged tumour region. The study also discusses the effects of certain factors on tumour growth, including the density and configuration of preexisting vessel networks and the blood oxygen content. The model enables us to examine the relationship between early tumour growth and hypoxic micro-environment in host tissues, which can be useful for further applications, such as tumour metastasis and the initialization of tumour angiogenesis.

Epithelial-mesenchymal transition in oral squamous carcinoma cells

In epithelial-mesenchymal transition (EMT), epithelial cells acquire traits typical for mesenchymal cells, dissociate their cell-cell junctions and gain the ability to migrate. EMT is essential during embryogenesis, but may also mediate cancer progression. Basement membranes are sheets of extracellular matrix that support epithelial cells. They have a major role in maintaining the epithelial phenotype and, in cancer, preventing cell migration, invasion and metastasis. Laminins are the main components of basement membranes and may actively contribute to malignancy. We first evaluated the differences between cell lines obtained from oral squamous cell carcinoma and its recurrence. As the results indicated a change from epithelial to fibroblastoid morphology, E-cadherin to N-cadherin switch, and change in expression of cytokeratins to vimentin intermediate filaments, we concluded that these cells had undergone EMT. We further induced EMT in primary tumour cells to gain knowledge of the effects of transcription factor Snail in this cell model. The E-cadherin repressors responsible for the EMT in these cells were ZEB-1, ZEB-2 and Snail, and ectopic expression of Snail was able to augment the levels of ZEB-1 and ZEB-2. We produced and characterized two monoclonal antibodies that specifically recognized Snail in cell lines and patient samples. By immunohistochemistry, Snail protein was found in mesenchymal tissues during mouse embryonal development, in fibroblastoid cells of healing skin wounds and in fibromatosis and sarcoma specimens. Furthermore, Snail localized to the stroma and borders of tumour cell islands in colon adenocarcinoma, and in laryngeal and cervical squamous cell carcinomas. Immunofluorescence labellings, immunoprecipitations and Northern and Western blots showed that EMT induced a progressive downregulation of laminin-332 and laminin-511 and, on the other hand, an induction of mesenchymal laminin-411. Chromatin immunoprecipitation revealed that Snail could directly bind upstream to the transcription start sites of both laminin α5 and α4 chain genes, thus regulating their expression. The levels of integrin α6β4, a receptor for laminin-332, as well as the hemidesmosomal complex proteins HD1/plectin and BP180 were downregulated in EMT-experienced cells. The expression of Lutheran glycoprotein, a specific receptor for laminin-511, was diminished, whereas the levels of integrins α6β1 and α1β1 and integrin-linked kinase were increased. In quantitative cell adhesion assays, the cells adhered potently to laminin-511 and fibronectin, but only marginally to laminin-411. Western blots and immunoprecipitations indicated that laminin-411 bound to fibronectin and could compromise cell adhesion to fibronectin in a dose-dependent manner. EMT induced a highly migratory and invasive tendency in oral squamous carcinoma cells. Actin-based adhesion and invasion structures, podosomes and invadopodia, were detected in the basal cell membranes of primary tumour and spontaneously transformed cancer cells, respectively. Immunofluorescence labellings showed marked differences in their morphology, as podosomes organized a ring structure with HD1/plectin, αII-spectrin, talin, focal adhesion kinase and pacsin 2 around the core filled with actin, cortactin, vinculin and filamin A. Invadopodia had no division between ring and core and failed to organize the ring proteins, but instead assembled tail-like, narrow actin cables that showed a talin-tensin switch. Time-lapse live-cell imaging indicated that both podosomes and invadopodia were long-lived entities, but the tails of invadopodia vigorously propelled in the cytoplasm and were occasionally released from the cell membrane. Invadopodia could also be externalized outside the cytoplasm, where they still retained the ability to degrade matrix. In 3D confocal imaging combined with in situ gelatin zymography, the podosomes of primary tumour cells were large, cylindrical structures that increased in time, whereas the invadopodia in EMT-driven cells were smaller, but more numerous and degraded the underlying matrix in significantly larger amounts. Fluorescence recovery after photobleaching revealed that the substructures of podosomes were replenished more rapidly with new molecules than those of invadopodia. Overall, our results indicate that EMT has a major effect on the transcription and synthesis of both intra- and extracellular proteins, including laminins and their receptors, and on the structure and dynamics of oral squamous carcinoma cells.

3D extracellular matrix interactions modulate tumour cell growth, invasion and angiogenesis in engineered tumour microenvironments

Interactions between tumour cells and extracellular matrix proteins of the tumour microenvironment play crucial roles in cancer progression. So far, however, there are only a few experimental platforms available that allow us to study these interactions systematically in a mechanically defined three-dimensional (3D) context. Here, we have studied the effect of integrin binding motifs found within common extracellular matrix (ECM) proteins on 3D breast (MCF-7) and prostate (PC-3, LNCaP) cancer cell cultures, and co-cultures with endothelial and mesenchymal stromal cells. For this purpose, matrix metalloproteinase-degradable biohybrid poly(ethylene) glycol-heparin hydrogels were decorated with the peptide motifs RGD, GFOGER (collagen I), or IKVAV (laminin-111). Over 14 days, cancer spheroids of 100-200µm formed. While the morphology of poorly invasive MCF-7 and LNCaP cells was not modulated by any of the peptide motifs, the aggressive PC-3 cells exhibited an invasive morphology when cultured in hydrogels comprising IKVAV and GFOGER motifs compared to RGD motifs or nonfunctionalised controls. PC-3 (but not MCF-7 and LNCaP) cell growth and endothelial cell infiltration were also significantly enhanced in IKVAV and GFOGER presenting gels. Taken together, we have established a 3D culture model that allows for dissecting the effect of biochemical cues on processes relevant to early cancer progression. These findings provide a basis for more mechanistic studies that may further advance our understanding of how ECM modulates cancer cell invasion and how to ultimately interfere with this process.

Prognostic importance of the tumour microenvironment in follicular lymphoma patients treated with immunochemotherapy

Follicular lymphoma (FL) is the second most common non-Hodgkin lymphoma. It is an indolent and clinically heterogeneous disease, which is generally considered incurable. Currently, immunochemotherapy has significantly improved the outcome of FL patients. This is based on the combination of rituximab, a monoclonal anti-CD20 antibody, with chemotherapy, and is used at present as a standard first-line therapy in FL. Thus far, however, patients have been selected for treatment based on clinical risk factors and indices that were developed before the rituximab era. Therefore, there is a growing need to understand the molecular mechanisms underlying the disease, which would not only provide information to predict survival in the rituximab era, but also enable the design of more targeted therapeutic strategies. In this study, our aim was to identify genes predicting the outcome in FL patients treated with immunochemotherapy. Thus, we performed a cDNA microarray with 24 FL patients. When gene expression differences from diagnostic tumour samples were related to the clinical outcome, we identified novel genes with a prognostic impact on survival. The expression of selected genes was further characterized with quantitative PCR and immunohistochemistry (IHC). Interestingly, the prognostic influence of these genes was often associated with their expression in non-malignant cells instead of tumour cells. Based on the observed gene expression patterns, we analyzed the abundance and prognostic value of non-malignant immune cells in 95-98 FL patients treated with immunochemotherapy. We observed that a high content of tumour-associated macrophages was a marker of a favourable prognosis. In contrast, the accumulation of mast cells correlated with a poor outcome and was further associated with tumour vascularity. Increased microvessel density also correlated with an inferior outcome. In addition, we used the same microarray data with a systems biology approach to identify signalling pathways or groups of genes capable of separating patients with favourable or adverse outcomes. Among the transcripts, there were many genes associated with signal transducers and activators of the transcription (STAT5a) pathway. When IHC was used as validation, STAT5a expression was mostly observed in T-cells and follicular dendritic cells, and expression was found to predict a favourable outcome. In cell cultures, rituximab was observed to induce the expression of STAT5a-associated interleukins in human lymphoma cell lines, which might provide a possible link for the cross-talk between rituximab-induced FL cells and their microenvironment. In conclusion, we have demonstrated that the microenvironment has a prognostic role in FL patients treated with immunochemotherapy. The results also address the importance of re-evaluating the prognostic markers in the rituximab era of lymphoma therapies.

Deformability Measurement of Single-Cells at High-Throughput With Imaging Flow Cytometry

Disease conditions like malaria, sickle cell anemia, diabetes mellitus, cancer, etc., are known to significantly alter the deformability of certain types of cells (red blood cells, white blood cells, circulating tumor cells, etc.). To determine the cellular deformability, techniques like micropipette aspiration, atomic force microscopy, optical tweezers, quantitative phase imaging have been developed. Many of these techniques have an advantage of determining the single cell deformability with ultrahigh precision. However, the suitability of these techniques for the realization of a deformability based diagnostic tool is questionable as they are expensive and extremely slow to operate on a huge population of cells. In this paper, we propose a technique for high-throughput (800 cells/s) determination of cellular deformability on a single cell basis. This technique involves capturing the image(s) of cells in flow that have undergone deformation under the influence of shear gradient generated by the fluid flowing through the microfluidic channels. Deformability indices of these cells can be computed by performing morphological operations on these images. We demonstrate the applicability of this technique for examining the deformability index on healthy, diabetic, and sphered red blood cells. We believe that this technique has a strong role to play in the realization of a potential tool that uses deformability as one of the important criteria in disease diagnosis.

Endoplasmic reticulum targeting tumour selective photocytotoxic oxovanadium(IV) complexes having vitamin-B6 and acridinyl moieties

Oxovanadium(IV) complexes of vitamin-B6 Schiff base, viz., VO(HL1/L-2/L-3)(B)] Cl (1-4), where B is 2,2'-bipyridine (bpy in 1 and 2), 11-(9-acridinyl)dipyrido3,2-a:2',3'-c]phenazine (acdppz in 3 and 4), H2L1 center dot HCl is 3-hydroxy-5-(hydroxymethyl)-4-(((2-hydroxyphenyl)imino)methyl)-2-methylp yridin-1-ium chloride (in 1 and 4), HL2 is 2-(((2-(1H-imidazol-4-yl)ethyl) imino)methyl) phenol (in 2) and HL3 is 4-(((2-(1H-imidazol-4- yl)ethyl)imino)methyl)-5-(hydroxymethyl)-2-methylpyridin-3-ol (in 3) were synthesized, characterized and their cellular uptake, photo-activated cytotoxicity and intracellular localization were studied. Complexes 1a, as the perchlorate salt of 1, and 2a, as the hexafluorophosphate salt of 2, were structurally characterized. Vitamin-B6 transporting membrane carrier (VTC) mediated entry into tumour cells in preference to the normal ones seems to be responsible for the higher cellular uptake of the complexes into HeLa and MCF-7 cells over MCF-10A cells. Complexes 3 and 4 having acdppz as the photosensitizer exhibit remarkable photocytotoxicity in these cancer cells giving IC50 of < 0.9 mu M. The complexes remain non-toxic in the dark. The complexes show photo-induced apoptotic cell death via singlet oxygen (O-1(2)) generation. Fluorescence microscopy reveals specific localization of complex 4 to endoplasmic reticulum (ER) and generation of O-1(2) possibly leads to apoptotic cell death by triggering ER stress response (ERSR).

Endoplasmic reticulum targeting tumour selective photocytotoxic oxovanadium(IV) complexes having vitamin-B6 and acridinyl moieties

Oxovanadium(IV) complexes of vitamin-B6 Schiff base, viz., VO(HL1/L-2/L-3)(B)] Cl (1-4), where B is 2,2'-bipyridine (bpy in 1 and 2), 11-(9-acridinyl)dipyrido3,2-a:2',3'-c]phenazine (acdppz in 3 and 4), H2L1 center dot HCl is 3-hydroxy-5-(hydroxymethyl)-4-(((2-hydroxyphenyl)imino)methyl)-2-methylp yridin-1-ium chloride (in 1 and 4), HL2 is 2-(((2-(1H-imidazol-4-yl)ethyl) imino)methyl) phenol (in 2) and HL3 is 4-(((2-(1H-imidazol-4- yl)ethyl)imino)methyl)-5-(hydroxymethyl)-2-methylpyridin-3-ol (in 3) were synthesized, characterized and their cellular uptake, photo-activated cytotoxicity and intracellular localization were studied. Complexes 1a, as the perchlorate salt of 1, and 2a, as the hexafluorophosphate salt of 2, were structurally characterized. Vitamin-B6 transporting membrane carrier (VTC) mediated entry into tumour cells in preference to the normal ones seems to be responsible for the higher cellular uptake of the complexes into HeLa and MCF-7 cells over MCF-10A cells. Complexes 3 and 4 having acdppz as the photosensitizer exhibit remarkable photocytotoxicity in these cancer cells giving IC50 of < 0.9 mu M. The complexes remain non-toxic in the dark. The complexes show photo-induced apoptotic cell death via singlet oxygen (O-1(2)) generation. Fluorescence microscopy reveals specific localization of complex 4 to endoplasmic reticulum (ER) and generation of O-1(2) possibly leads to apoptotic cell death by triggering ER stress response (ERSR).