Evolution of cell motility in an individual-based model of tumour growth

Tumour invasion is driven by proliferation and importantly migration into the surrounding tissue. Cancer cell motility is also critical in the formation of metastases and is therefore a fundamental issue in cancer research. In this paper we investigate the emergence of cancer cell motility in an evolving tumour population using an individual-based modelling approach. In this model of tumour growth each cell is equipped with a micro-environment response network that determines the behaviour or phenotype of the cell based on the local environment. The response network is modelled using a feed-forward neural network, which is subject to mutations when the cells divide. With this model we have investigated the impact of the micro-environment on the emergence of a motile invasive phenotype. The results show that when a motile phenotype emerges the dynamics of the model are radically changed and we observe faster growing tumours exhibiting diffuse morphologies. Further we observe that the emergence of a motile subclone can occur in a wide range of micro-environmental growth conditions. Iterated simulations showed that in identical growth conditions the evolutionary dynamics either converge to a proliferating or migratory phenotype, which suggests that the introduction of cell motility into the model changes the shape of fitness landscape on which the cancer cell population evolves and that it now contains several local maxima. This could have important implications for cancer treatments which focus on the gene level, as our results show that several distinct genotypes and critically distinct phenotypes can emerge and become dominant in the same micro-environment.     

Strategies of Eradicating Glioma Cells: A Multi-Scale Mathematical Model with MiR-451-AMPK-mTOR Control

The cellular dispersion and therapeutic control of glioblastoma, the most aggressive type of primary brain cancer, depends critically on the migration patterns after surgery and intracellular responses of the individual cancer cells in response to external biochemical and biomechanical cues in the microenvironment. Recent studies have shown that a particular microRNA, miR-451, regulates downstream molecules including AMPK and mTOR to determine the balance between rapid proliferation and invasion in response to metabolic stress in the harsh tumor microenvironment. Surgical removal of main tumor is inevitably followed by recurrence of the tumor due to inaccessibility of dispersed tumor cells in normal brain tissue. In order to address this multi-scale nature of glioblastoma proliferation and invasion and its response to conventional treatment, we propose a hybrid model of glioblastoma that analyses spatio-temporal dynamics at the cellular level, linking individual tumor cells with the macroscopic behaviour of cell organization and the microenvironment, and with the intracellular dynamics of miR-451-AMPK-mTOR signaling within a tumour cell. The model identifies a key mechanism underlying the molecular switches between proliferative phase and migratory phase in response to metabolic stress and biophysical interaction between cells in response to fluctuating glucose levels in the presence of blood vessels (BVs). The model predicts that cell migration, therefore efficacy of the treatment, not only depends on oxygen and glucose availability but also on the relative balance between random motility and strength of chemoattractants. Effective control of growing cells near BV sites in addition to relocalization of invisible migratory cells back to the resection site was suggested as a way of eradicating these migratory cells.     

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.     

Cell kinetics in a tumour cord

In some tumours, the viable cells grow around blood vessels forming cylindrical structures called tumour cords, which are surrounded by regions of necrosis. In the present paper, we propose a mathematical model for the cell kinetics in a tumour cord at the stationary state. Both proliferating cells and quiescent cells are considered, and the proliferating cell population is structured by age. Cell migration towards cord periphery is accounted for from a continuum viewpoint. The age distribution of proliferating cells, the fraction of cells in S phase, the growth fraction and the velocity along the cord radius are computed. The predictions of the model are compared with literature data obtained from two experimental rat hepatomas. The model was used to compute the profile of the oxygen tension within the cord. Possible modifications and extensions are also presented.     

Hybrid mathematical model of glioma progression

Objectives:  Gliomas are an important form of brain cancer, with high mortality rate. Mathematical models are often used to understand and predict their behaviour. However, using current modeling techniques one must choose between simulating individual cell behaviour and modeling tumours of clinically significant size.
Materials and Methods:  We propose a hybrid compartment-continuum-discrete model to simulate glioma growth and malignant cell invasion. The discrete portion of the model is capable of capturing intercellular interactions, including cell migration, intercellular communication, spatial cell population heterogeneity, phenotype differentiation, epigenetic events, proliferation, and apoptosis. Combining this with a compartment and continuum model allows clinically significant tumour sizes to be evaluated.
Results and Conclusions:  This model is used to perform multiple simulations to determine sensitivity to changes in important model parameters, specifically, the fundamental length parameter, necrotic cell degradation rate, rate of cell migration, and rate of phenotype transformation. Using these values, the model is able to simulate tumour growth and invasion behaviour, observed clinically. This mathematical model provides a means to simulate various tumour development scenarios, which may lead to a better understanding of how altering fundamental parameters can influence neoplastic progression.     

Mesenchymal stem cells promote cell invasion and migration and autophagy‐induced epithelial‐mesenchymal transition in A549 lung adenocarcinoma cells

Mesenchymal stem cells (MSCs) are recruited into the tumour microenvironment and promote tumour growth and metastasis. Tumour microenvironment‐induced autophagy is considered to suppress primary tumour formation by impairing migration and invasion. Whether these recruited MSCs regulate tumour autophagy and whether autophagy affects tumour growth are controversial. Our data showed that MSCs promote autophagy activation, reactive oxygen species production, and epithelial‐mesenchymal transition (EMT) as well as increased migration and invasion in A549 cells. Decreased expression of E‐cadherin and increased expression of vimentin and Snail were observed in A549 cells cocultured with MSCs. Conversely, MSC coculture‐mediated autophagy positively promoted tumour EMT. Autophagy inhibition suppressed MSC coculture‐mediated EMT and reduced A549 cell migration and invasion slightly. Furthermore, the migratory and invasive abilities of A549 cells were additional increased when autophagy was further enhanced by rapamycin treatment. Taken together, this work suggests that microenvironments containing MSCs can promote autophagy activation for enhancing EMT; MSCs also increase the migratory and invasive abilities of A549 lung adenocarcinoma cells. Mesenchymal stem cell‐containing microenvironments and MSC‐induced autophagy signalling may be potential targets for blocking lung cancer cell migration and invasion.     

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 mathematical analysis of a model for tumour angiogenesis

In order to accomplish the transition from avascular to vascular growth, solid tumours secrete a diffusible substance known as tumour angiogenesis factor (TAF) into the surrounding tissue. Neighbouring endothelial cells respond to this chemotactic stimulus in a well-ordered sequence of events comprising, at minimum, of a degradation of their basement membrane, migration and proliferation. A mathematical model is presented which takes into account two of the most important events associated with the endothelial cells as they form capillary sprouts and make their way towards the tumour i.e. cell migration and proliferation. The numerical simulations of the model compare very well with the actual experimental observations. We subsequently investigate the model analytically by making some relevant biological simplifications. The mathematical analysis helps to clarify the particular contributions to the model of the two independent processes of endothelial cell migration and proliferation.     

Examining Go-or-Grow Using Fluorescent Cell-Cycle Indicators and Cell-Cycle-Inhibiting Drugs

The go-or-grow hypothesis states that adherent cells undergo reversible phenotype switching between migratory and proliferative states, with cells in the migratory state being more motile than cells in the proliferative state. Here, we examine go-or-grow in two-dimensional in vitro assays using melanoma cells with fluorescent cell-cycle indicators and cell-cycle-inhibiting drugs. We analyze the experimental data using single-cell tracking to calculate mean diffusivities and compare motility between cells in different cell-cycle phases and in cell-cycle arrest. Unequivocally, our analysis does not support the go-or-grow hypothesis. We present clear evidence that cell motility is independent of the cell-cycle phase and that nonproliferative arrested cells have the same motility as cycling cells.     

Loss of the integrin-activating transmembrane protein Fam38A (Piezo1) promotes a switch to a reduced integrin-dependent mode of cell migration

Lung cancer is one of the most common fatal diseases in the developed world. The disease is rarely cured by currently available therapies, with an overall survival rate of ～10%. Characterizing novel proteins that offer crucial insights into the processes of lung tumour invasion and metastasis may therefore provide much-needed prognostic markers, and influence therapeutic strategies. Aberrant function of the integrin family of heterodimeric cell surface receptors is a common theme in cancer--investigation into novel integrin activity regulators may offer crucial insights into the processes of tumour invasion and metastasis and may reveal insights into potential therapeutic targets. We previously described that depletion of the novel multi-transmembrane domain protein Fam38A, located at the endoplasmic reticulum (ER), inactivates endogenous beta1 integrin affinity, reducing cell adhesion. We now show that depletion of Fam38A, also now known as Piezo1, causes anchorage independence and a switch to a reduced integrin-dependent mode of cell migration/invasion, a novel phenotype for this integrin-regulating protein. Normal lung epithelial cells show increased rates of migration by 2D time-lapse microscopy and increased capacity to invade into matrigel, despite having decreased integrin affinity. We confirm greatly depleted Fam38A expression in small cell lung cancer (SCLC) lines where a form of reduced integrin-dependent migration, i.e. amoeboid migration, is a known phenotype. We propose that loss of Fam38A expression may cause increased cell migration and metastasis in lung tumours.     

Using real-time impedance-based assays to monitor the effects of fibroblast-derived media on the adhesion,proliferation, migration and invasion of colon cancer cells

Increasing our knowledge of the mechanisms regulating cell proliferation, migration and invasion are central to understanding tumour progression and metastasis. The local tumour microenvironment contributes to the transformed phenotype in cancer by providing specific environmental cues that alter the cells behaviour and promotes metastasis. Fibroblasts have a strong association with cancer and in recent times there has been some emphasis in designing novel therapeutic strategies that alter fibroblast behaviour in the tumour microenvironment. Fibroblasts produce growth factors, chemokines and many of the proteins laid down in the ECM (extracellular matrix) that promote angiogenesis, inflammation and tumour progression. In this study, we use a label-free RTCA (real-time cell analysis) platform (xCELLigence) to investigate how media derived from human fibroblasts alters cancer cell behaviour. We used a series of complimentary and novel experimental approaches to show HCT116 cells adhere, proliferate and migrate significantly faster in the presence of media from human fibroblasts. As well as this, we used the xCELLigence CIM-plates system to show that HCT116 cells invade matrigel layers aggressively when migrating towards media derived from human fibroblasts. These data strongly suggest that fibroblasts have the ability to increase the migratory and invasive properties of HCT116 cells. This is the first study that provides real-time data on fibroblast-mediated migration and invasion kinetics of colon cancer cells.     

Experimental chemotherapy and concepts related to the cell cycle

Scheduling of chemotherapy is limited by damage to normal tissues, and tolerated schedules are dependent on normal tissue recovery. Most anticancer drugs are more toxic to proliferating cells and the fall and recovery of granulocyte counts after chemotherapy may be explained by the effect of drugs on rapidly proliferating precursor cells in the bone marrow. It is argued that serious toxicity due to myelosuppression most often occurs because of damage to proliferating precursors that may be recognized in bone marrow rather than to stem cells. In contrast, therapy that is aimed at producing cure or long-term remission of tumours must be directed at killing tumour stem cells. The evidence that tumours contain a limited population of cells which can repopulate the tumour after treatment (and are therefore tumour stem cells) is reviewed critically. While there is quite strong evidence for a limited population of target cells, evidence from studies on metastases suggests that the tumour cells which may express this stem cell property may change with time. The stem cell concept has major implications for predictive assays. Although colony-forming assays appear to have a sound biological background for predicting tumour response, technical problems prevent them from being used routinely in patient management. Cells in tumours are known to be heterogeneous and at least three types of heterogeneity may influence tumour response to drug treatment: the development of subclones with differing properties including drug resistance; variation in cellular properties due to differentiation during clonal expansion; and variation in properties due to nutritional status and micro-anatomy. Heterogeneity in drug distribution within solid tumours may occur because of limited drug penetration from blood vessels, and nutrient-deprived cells in solid tumours may be expected to escape the toxicity of some anticancer drugs as well as being resistant to radiation because of hypoxia. This may occur both because nutrient-deprived cells have a low rate of cell proliferation, and also because of poor drug penetration to them. There is a need for improved understanding of the mechanisms that lead to cell death in tumours. If these mechanisms were understood, it might be possible to simulate them by therapeutic manoeuvres. Recent research from our laboratory suggests that the combination of low extracellular pH and hypoxia may be very toxic to cells in nutrient-deprived regions. Drugs which limit the cell's ability to survive in regions of acid pH may provide strategy for therapy of nutrient-deprived cells.     

Combining Gompertzian growth and cell population dynamics

A two-compartment model of cancer cells population dynamics proposed by Gyllenberg and Webb includes transition rates between proliferating and quiescent cells as non-specified functions of the total population, N. We define the net inter-compartmental transition rate function: Phi(N). We assume that the total cell population follows the Gompertz growth model, as it is most often empirically found and derive Phi(N). The Gyllenberg-Webb transition functions are shown to be characteristically related through Phi(N). Effectively, this leads to a hybrid model for which we find the explicit analytical solutions for proliferating and quiescent cell populations, and the relations among model parameters. Several classes of solutions are examined. Our model predicts that the number of proliferating cells may increase along with the total number of cells, but the proliferating fraction appears to be a continuously decreasing function. The net transition rate of cells is shown to retain direction from the proliferating into the quiescent compartment. The death rate parameter for quiescent cell population is shown to be a factor in determining the proliferation level for a particular Gompertz growth curve.     

Border-cell migration: the race is on

The conversion of stationary epithelial cells into migratory, invasive cells is important for normal embryonic development and tumour metastasis. Border-cell migration in the ovary of Drosophila melanogaster has emerged as a simple, genetically tractable model for studying this process. Three distinct signals, which are also upregulated in cancer, control border-cell migration, so identifying further genes that are involved in border-cell migration could provide new insights into tumour invasion.     

Differing modes of tumour cell invasion have distinct requirements for Rho/ROCK signalling and extracellular proteolysis

Rho family GTPases regulate the cytoskeleton and cell migration and are frequently overexpressed in tumours. Here, we identify two modes of tumour-cell motility in 3D matrices that involve different usage of Rho signalling. Rho signalling through ROCK promotes a rounded bleb-associated mode of motility that does not require pericellular proteolysis. This form of motility requires ezrin, which is localized in the direction of cell movement. In contrast, elongated cell motility is associated with Rac-dependent F-actin-rich protrusions and does not require Rho, ROCK or ezrin function. Combined blockade of extracellular proteases and ROCK negates the ability of tumour cells to switch between modes of motility and synergises to prevent tumour cell invasion.     

Splicing factor hnRNPH drives an oncogenic splicing switch in gliomas

In tumours, aberrant splicing generates variants that contribute to multiple aspects of tumour establishment, progression and maintenance. We show that in glioblastoma multiforme (GBM) specimens, death-domain adaptor protein Insuloma-Glucagonoma protein 20 (IG20) is consistently aberrantly spliced to generate an antagonist, anti-apoptotic isoform (MAP-kinase activating death domain protein, MADD), which effectively redirects TNF-α/TRAIL-induced death signalling to promote survival and proliferation instead of triggering apoptosis. Splicing factor hnRNPH, which is upregulated in gliomas, controls this splicing event and similarly mediates switching to a ligand-independent, constitutively active Recepteur d'Origine Nantais (RON) tyrosine kinase receptor variant that promotes migration and invasion. The increased cell death and the reduced invasiveness caused by hnRNPH ablation can be rescued by the targeted downregulation of IG20/MADD exon 16- or RON exon 11-containing variants, respectively, using isoform-specific knockdown or splicing redirection approaches. Thus, hnRNPH activity appears to be involved in the pathogenesis and progression of malignant gliomas as the centre of a splicing oncogenic switch, which might reflect reactivation of stem cell patterns and mediates multiple key aspects of aggressive tumour behaviour, including evasion from apoptosis and invasiveness.     

Resveratrol inhibits hepatocellular carcinoma progression driven by hepatic stellate cells by targeting Gli-1

A disintegrin and metalloproteinase 17 (ADAM17) is highly expressed in various tumours and affects tumour progression. In this study, ADAM17 expression in 60 gastric cancer and 20 normal gastric mucosal tissues was assessed using immunohistochemistry. ADAM17 expression was higher in gastric cancer tissues than in normal gastric mucosal tissues (P < 0.0005). A significant relationship was identified between ADAM17 expression and the depth of tumour invasion, metastasis, and carcinoma stage. Furthermore, the effects of ADAM17 knockdown on the proliferation, cell invasion, and apoptosis of human gastric carcinoma cells (SGC-7901) were determined. SGC-7901 cells were transfected with ADAM17-shRNA, and cell proliferation and migration were assessed using CCK-8 and transwell assays, respectively, to evaluate the role of ADAM17 in tumour proliferation and invasion. Furthermore, the EGFR signalling pathway, the cell membrane receptor-bound TNF-α level, and apoptosis were evaluated by western blotting and flow cytometry. The inhibition of cell proliferation and invasion was observed in the ADAM17 knockdown cells, which was associated with modulation of the EGFR signalling pathway. Apoptosis was increased, and TNF-α signalling was attenuated in the ADAM17 knockdown cells. Our study demonstrated that ADAM17 over-expression in gastric cancer tissues was closely associated with tumour proliferation, invasion, and apoptosis.     

FGF signals for cell proliferation and migration through different pathways

FGFs are pleiotropic growth factors that control cell proliferation, migration and differentiation. However, FGF transduction studies have so far focused primarily on the mitogenic effect of this growth factor family and it has been difficult to assess if the described intracellular signaling pathways are dedicated solely to cell proliferation, or whether they are equally important for the migratory activity often seen in responsive cells. We review here papers in which the migratory effects of this growth factor family were clearly discriminated from proliferative effects. In toto, these studies suggest that cells use different signaling pathways for migration, such as Src and p38 MAP kinase, from those for proliferation, which tend to upregulate the ERKs. Which signaling pathway a cell uses for proliferation or migration appears to depend on many factors, including the structure and the quantity of available FGF trapped in the basal lamina by heparan sulfate co-factors, the disposition of cognate high affinity receptors and the general environment of the cell. Thus the density of the cell population, the state of the cell cycle, the presence of other factors or receptors will modulate the migratory response of cells to FGF.     

Regulatory domain selectivity in the cell-type specific PKN-dependence of cell migration

The mammalian protein kinase N (PKN) family of Serine/Threonine kinases comprises three isoforms, which are targets for Rho family GTPases. Small GTPases are major regulators of the cellular cytoskeleton, generating interest in the role(s) of specific PKN isoforms in processes such as cell migration and invasion. It has been reported that PKN3 is required for prostate tumour cell invasion but not PKN1 or 2. Here we employ a cell model, the 5637 bladder tumour cell line where PKN2 is relatively highly expressed, to assess the potential redundancy of these isoforms in migratory responses. It is established that PKN2 has a critical role in the migration and invasion of these cells. Furthermore, using a PKN wild-type and chimera rescue strategy, it is shown that PKN isoforms are not simply redundant in supporting migration, but appear to be linked through isoform specific regulatory domain properties to selective upstream signals. It is concluded that intervention in PKNs may need to be directed at multiple isoforms to be effective in different cell types.     

Mathematical modelling of the influence of heat shock proteins on cancer invasion of tissue

Tumour cell invasion is crucial for cancer metastasis, which is the main cause of cancer mortality. An important group of proteins involved in cancer invasion are the Heat Shock Proteins (HSPs). According to experimental data, inhibition of one of these proteins, Hsp90, slows down cancer cells while they are invading tissue, but does not affect the synthesis of matrix metalloproteinases (MMP2 and MMP9), which are very important for cancer metastasis, acting as extracellular matrix (ECM) degrading enzymes. To test different biological hypotheses regarding how precisely Hsp90 influences tumour invasion, in this paper we use a model of solid tumour growth which accounts for the interactions between Hsp90 dynamics and the migration of cancer cells and, alternatively, between Hsp90 dynamics and the synthesis of matrix degrading enzymes (MDEs). The model consists of a system of reaction-diffusion-taxis partial differential equations describing interactions between cancer cells, MDE, and the host tissue (ECM). Using numerical simulations we investigate the effects of the administration of Hsp90 inhibitors on the dynamics of tumour invasion. Alternative mechanisms of reduction of cancer invasiveness result in different simulated patterns of the invading tumour cells. Therefore, predictions of the model suggest experiments which might be performed to develop a deeper understanding of the tumour invasion process.