A hybrid cellular automaton model of clonal evolution in cancer: the emergence of the glycolytic phenotype

We present a cellular automaton model of clonal evolution in cancer aimed at investigating the emergence of the glycolytic phenotype. In the model 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. This implies that cells might react differently to the environment and when space and nutrients are limited only the fittest cells will survive. With this model we have investigated the impact of the environment on the growth dynamics of the tumour. In particular, we have analysed the influence of the tissue oxygen concentration and extra-cellular matrix density on the dynamics of the model. We found that the environment influences both the growth and the evolutionary dynamics of the tumour. For low oxygen concentration we observe tumours with a fingered morphology, while increasing the matrix density gives rise to more compact tumours with wider fingers. The distribution of phenotypes in the tumour is also affected, and we observe that the glycolytic phenotype is most likely to emerge in a poorly oxygenated tissue with a high matrix density. Our results suggest that it is the combined effect of the oxygen concentration and matrix density that creates an environment where the glycolytic phenotype has a growth advantage and consequently is most likely to appear.     

Modelling evolutionary cell behaviour using neural networks: Application to tumour growth

In this paper, we present a modelling framework for cellular evolution that is based on the notion that a cell’s behaviour is driven by interactions with other cells and its immediate environment. We equip each cell with a phenotype that determines its behaviour and implement a decision mechanism to allow evolution of this phenotype. This decision mechanism is modelled using feed-forward neural networks, which have been suggested as suitable models of cell signalling pathways. The environmental variables are presented as inputs to the network and result in a response that corresponds to the phenotype of the cell. The response of the network is determined by the network parameters, which are subject to mutations when the cells divide. This approach is versatile as there are no restrictions on what the input or output nodes represent, they can be chosen to represent any environmental variables and behaviours that are of importance to the cell population under consideration. This framework was implemented in an individual-based model of solid tumour growth in order to investigate the impact of the tissue oxygen concentration on the growth and evolutionary dynamics of the tumour. Our results show that the oxygen concentration affects the tumour at the morphological level, but more importantly has a direct impact on the evolutionary dynamics. When the supply of oxygen is limited we observe a faster divergence away from the initial genotype, a higher population diversity and faster evolution towards aggressive phenotypes. The implementation of this framework suggests that this approach is well suited for modelling systems where evolution plays an important role and where a changing environment exerts selection pressure on the evolving population.     

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.     

Reoxygenation and Split-Dose Response to Radiation in a Tumour Model with Krogh-Type Vascular Geometry

After a single dose of radiation, transient changes caused by cell death are likely to occur in the oxygenation of surviving cells. Since cell radiosensitivity increases with oxygen concentration, reoxygenation is expected to increase the sensitivity of the cell population to a successive irradiation. In previous papers we proposed a model of the response to treatment of tumour cords (cylindrical arrangements of tumour cells growing around a blood vessel of the tumour). The model included the motion of cells and oxygen diffusion and consumption. By assuming parallel and regularly spaced tumour vessels, as in the Krogh model of microcirculation, we extend our previous model to account for the action of irradiation and the damage repair process, and we study the time course of the oxygenation and the cellular response. By means of simulations of the response to a dose split in two equal fractions, we investigate the dependence of tumour response on the time interval between the fractions and on the main parameters of the system. The influence of reoxygenation on a therapeutic index that compares the effect of a split dose on the tumour and on the normal tissue is also investigated.     

A cellular automaton model for tumour growth in inhomogeneous environment

Most of the existing mathematical models for tumour growth and tumour-induced angiogenesis neglect blood flow. This is an important factor on which both nutrient and metabolite supply depend. In this paper we aim to address this shortcoming by developing a mathematical model which shows how blood flow and red blood cell heterogeneity influence the growth of systems of normal and cancerous cells. The model is developed in two stages. First we determine the distribution of oxygen in a native vascular network, incorporating into our model features of blood flow and vascular dynamics such as structural adaptation, complex rheology and red blood cell circulation. Once we have calculated the oxygen distribution, we then study the dynamics of a colony of normal and cancerous cells, placed in such a heterogeneous environment. During this second stage, we assume that the vascular network does not evolve and is independent of the dynamics of the surrounding tissue. The cells are considered as elements of a cellular automaton, whose evolution rules are inspired by the different behaviour of normal and cancer cells. Our aim is to show that blood flow and red blood cell heterogeneity play major roles in the development of such colonies, even when the red blood cells are flowing through the vasculature of normal, healthy tissue.     

Angiogenesis and vascular remodelling in normal and cancerous tissues

Vascular development and homeostasis are underpinned by two fundamental features: the generation of new vessels to meet the metabolic demands of under-perfused regions and the elimination of vessels that do not sustain flow. In this paper we develop the first multiscale model of vascular tissue growth that combines blood flow, angiogenesis, vascular remodelling and the subcellular and tissue scale dynamics of multiple cell populations. Simulations show that vessel pruning, due to low wall shear stress, is highly sensitive to the pressure drop across a vascular network, the degree of pruning increasing as the pressure drop increases. In the model, low tissue oxygen levels alter the internal dynamics of normal cells, causing them to release vascular endothelial growth factor (VEGF), which stimulates angiogenic sprouting. Consequently, the level of blood oxygenation regulates the extent of angiogenesis, with higher oxygenation leading to fewer vessels. Simulations show that network remodelling (and de novo network formation) is best achieved via an appropriate balance between pruning and angiogenesis. An important factor is the strength of endothelial tip cell chemotaxis in response to VEGF. When a cluster of tumour cells is introduced into normal tissue, as the tumour grows hypoxic regions form, producing high levels of VEGF that stimulate angiogenesis and cause the vascular density to exceed that for normal tissue. If the original vessel network is sufficiently sparse then the tumour may remain localised near its parent vessel until new vessels bridge the gap to an adjacent vessel. This can lead to metastable periods, during which the tumour burden is approximately constant, followed by periods of rapid growth.     

Capturing the Dynamics of a Hybrid Multiscale Cancer Model with a Continuum Model

Cancer is a complex disease involving processes at spatial scales from subcellular, like cell signalling, to tissue scale, such as vascular network formation. A number of multiscale models have been developed to study the dynamics that emerge from the coupling between the intracellular, cellular and tissue scales. Here, we develop a continuum partial differential equation model to capture the dynamics of a particular multiscale model (a hybrid cellular automaton with discrete cells, diffusible factors and an explicit vascular network). The purpose is to test under which circumstances such a continuum model gives equivalent predictions to the original multiscale model, in the knowledge that the system details are known, and differences in model results can be explained in terms of model features (rather than unknown experimental confounding factors). The continuum model qualitatively replicates the dynamics from the multiscale model, with certain discrepancies observed owing to the differences in the modelling of certain processes. The continuum model admits travelling wave solutions for normal tissue growth and tumour invasion, with similar behaviour observed in the multiscale model. However, the continuum model enables us to analyse the spatially homogeneous steady states of the system, and hence to analyse these waves in more detail. We show that the tumour microenvironmental effects from the multiscale model mean that tumour invasion exhibits a so-called pushed wave when the carrying capacity for tumour cell proliferation is less than the total cell density at the tumour wave front. These pushed waves of tumour invasion propagate by triggering apoptosis of normal cells at the wave front. Otherwise, numerical evidence suggests that the wave speed can be predicted from linear analysis about the normal tissue steady state.     

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.     

Microenvironment driven invasion: a multiscale multimodel investigation

Cancer is a complex, multiscale process, in which genetic mutations occurring at a subcellular level manifest themselves as functional and morphological changes at the cellular and tissue scale. The importance of interactions between tumour cells and their microenvironment is currently of great interest in experimental as well as computational modelling. Both the immediate microenvironment (e.g. cell-cell signalling or cell-matrix interactions) and the extended microenvironment (e.g. nutrient supply or a host tissue structure) are thought to play crucial roles in both tumour progression and suppression. In this paper we focus on tumour invasion, as defined by the emergence of a fingering morphology, which has previously been shown to be dependent upon harsh microenvironmental conditions. Using three different modelling approaches at two different spatial scales we examine the impact of nutrient availability as a driving force for invasion. Specifically we investigate how cell metabolism (the intrinsic rate of nutrient consumption and cell resistance to starvation) influences the growing tumour. We also discuss how dynamical changes in genetic makeup and morphological characteristics, of the tumour population, are driven by extreme changes in nutrient supply during tumour development. The simulation results indicate that aggressive phenotypes produce tumour fingering in poor nutrient, but not rich, microenvironments. The implication of these results is that an invasive outcome appears to be co-dependent upon the evolutionary dynamics of the tumour population driven by the microenvironment.     

In vivo identification of bipotential adipocyte progenitors recruited by β3-adrenoceptor activation and high-fat feeding

Nutritional and pharmacological stimuli can dramatically alter the cellular phenotypes in white adipose tissue (WAT). Utilizing genetic lineage tracing techniques, we demonstrate that brown adipocytes (BA) that are induced by β3-adrenergic receptor activation in abdominal WAT arise from the proliferation and differentiation of cells expressing platelet-derived growth factor receptor alpha (PDGFRα), CD34, and Sca-1 (PDGFRα(+) cells). PDGFRα(+) cells have a unique morphology in which extended processes contact multiple cells in the tissue microenvironment. Surprisingly, these cells also give rise to white adipocytes (WA) that can comprise up to 25% of total fat cells in abdominal fat pads following 8?weeks of high-fat feeding. Isolated PDGFRα(+) cells differentiated into both BA and WA in?vitro and generated WA after transplantation in?vivo. The identification of PDGFRα(+) cells as bipotential adipocyte progenitors will enable further investigation of mechanisms that promote therapeutic cellular remodeling in adult WAT.     

The influence of entropic crowding in cell monolayers

Cell-cell interaction dictates cell morphology and organization, which play a crucial role in the micro-architecture of tissues that guides their biological and mechanical functioning. Here, we investigate the effect of cell density on the responses of cells seeded on flat substrates using a novel statistical thermodynamics framework. The framework recognizes the existence of nonthermal fluctuations in cellular response and thereby naturally captures entropic interactions between cells in monolayers. In line with observations, the model predicts that cell area and elongation decrease with increasing cell seeding density—both are a direct outcome of the fluctuating nature of the cellular response that gives rise to enhanced cell-cell interactions with increasing cell crowding. The modeling framework also predicts the increase in cell alignment with increasing cell density: this cellular ordering is also due to enhanced entropic interactions and is akin to nematic ordering in liquid crystals. Our simulations provide physical insights that suggest that entropic cell-cell interactions play a crucial role in governing the responses of cell monolayers.     

Clonal variation for tolerance to polyethylene glycol-induced water stress in cultured tomato cells

Cell clones were isolated from a population of cultured tomato (Lycopersicon esculentum Mill cv VFNT-cherry) cells and their tolerance to polyethylene glycol (PEG)-induced water stress was measured. Considerable variation for tolerance among the clones was found. Tolerance differences between clones appeared to be spontaneous and were different from tolerance differences between adapted and unadapted cells. Unlike adapted (selected by exposure to PEG) cells, cell clones retained their relative tolerance for many generations in the absence of selection pressure, and tolerance of both relatively tolerant and intolerant clones was very dependent on growth cycle stage and inoculum density. Analysis of subclones isolated from relatively tolerant and intolerant parent clones revealed that each parent clone gives rise to progeny with tolerances near the mean tolerance of both parents. However, progeny populations of both tolerant and intolerant parents are enriched with individuals with phenotypes nearer the mean response of their respective parent populations. When exposed to PEG, relatively tolerant and intolerant clones alike become adapted to the level of PEG to which they are exposed, and have the same phenotypic level of tolerance. Thus, selection by exposure to stress is unable to discriminate (on the basis of growth) between the innately tolerant and intolerant cell types within the population. This is indicated also by the fact that clones isolated from a population of cells adjusted to growth on 25% PEG do not show an enriched frequency of tolerant phenotypes when grown in the absence of PEG compared to the nonselected normal cell population which has never been adjusted to growth on PEG.     

Tumour angiogenesis normalized by myo-inositol trispyrophosphate alleviates hypoxia in the microenvironment and promotes antitumor immune response

Pathologic angiogenesis directly responds to tumour hypoxia and controls the molecular/cellular composition of the tumour microenvironment, increasing both immune tolerance and stromal cooperation with tumour growth. Myo-inositol-trispyrophosphate (ITPP) provides a means to achieve stable normalization of angiogenesis. ITPP increases intratumour oxygen tension (pO₂) and stabilizes vessel normalization through activation of endothelial Phosphatase-and-Tensin-homologue (PTEN). Here, we show that the tumour reduction due to the ITPP-induced modification of the tumour microenvironment by elevating pO₂ affects the phenotype and properties of the immune infiltrate. Our main observations are as follows: a relative change in the M1 and M2 macrophage-type proportions, increased proportions of NK and CD8⁺T cells, and a reduction in Tregs and Th2 cells. We also found, in vivo and in vitro, that the impaired access of PD1⁺NK cells to tumour cells is due to their adhesion to PD-L1⁺/PD-L2⁺ endothelial cells in hypoxia. ITPP treatment strongly reduced PD-L1/PD-L2 expression on CD45+/CD31+ cells, and PD1⁺ cells were more numerous in the tumour mass. CTLA-4⁺ cell numbers were stable, but level of expression decreased. Similarly, CD47⁺ cells and expression were reduced. Consequently, angiogenesis normalization induced by ITPP is the mean to revert immunosuppression into an antitumor immune response. This brings a key adjuvant effect to improve the efficacy of chemo/radio/immunotherapeutic strategies for cancer treatment.     

Head activator does not qualitatively alter head morphology in regenerates ofHydra oligactis

Summary The characterization of head activator (HA) as a morphogen capable of increasing the number of tentacles regenerated by hydra was re-examined. Gastric tissue was excised from HA-treated whole animals and allowed to regenerate. At the cellular level the differentiation of head-specific ectodermal epithelial cells was monitored by quantifying monoclonal antibody, CP8, labeling. This labeling has been correlated with a rise in head activation potential and the determination of tissue to form head structures (Javois et al. 1986). At the morphological level tentacle number was monitored. HA-treated regenerates began the head patterning processes and evaginated tentacles sooner than controls but did not produce extra tentacles. The kinetics of CP8 labeling did not reveal major differences between treated and control regenerates after the initiation of head-specific epithelial cell differentiation. HA appeared to act more like a growth factor stimulating the differentiation of head-specific cell types rather than a morphogen which altered head morphology. An additional aspect of the study examined axial-specific effects of HA on the initiation and extent of head-specific epithelial cell differentiation. The cellular response of ectodermal epithelial cells to HA was dependent on their original axial location. More CP8⁺ tissue differentiated in regenerates of apical as opposed to mid-gastric origin.     

Influence of hormone concentration and time factor on development of receptor memory in a unicellular (Tetrahymena) model system

1. Treatment of Tetrahymena pyriformis cells with diiodotyrosine (T2) gave rise to a considerable, concentration-dependent increase of the growth rate within the range of 10(-15) and 10(-9) M, but did not influence it at the level of 10(-18) M. 2. Re-exposure of the cells 1, 2 and 4 weeks later to the hormone concentrations originally used accounted for a marked increase of growth rate at all hormone levels tested, indicating that the extremely low concentration of 10(-18) M, which failed to stimulate growth on first exposure, did nevertheless give rise to hormonal imprinting, which caused the cells to "remember" the hormone, as judged from their increased responsiveness to it on re-exposure. 3. The degree of growth response was concentration-dependent on both first and second exposure: higher levels of treatment gave rise to firmer imprinting, and to greater response on re-exposure. 4. The length of exposure time proved to be more decisive than the level of treatment in respect of the development of hormonal imprinting. 5. Short-term exposures up to 60 min, although they stimulated cell growth by direct effect, gave rise to lasting inhibition of cellular response to re-exposure(s) rather than to hormonal imprinting.     

Oncogenes, anti-oncogenes and the immune response to cancer: a mathematical model.

We develop a mathematical model for the initial growth of a tumour after a mutation in which either an oncogene is expressed or an anti-oncogene (i.e. tumour suppressor gene) is lost. Our model incorporates mitotic control by several biochemicals, with quite different regulatory characteristics, and we consider mutations affecting the cellular response to these control mechanisms. Our mathematical representation of these mutations reflects the current understanding of the roles of oncogenes and anti-oncogenes in controlling cell proliferation. Numerical solutions of our model, for biologically relevant parameter values, show that the different types of mutations have quite different effects. Mutations affecting the cell response to chemical regulators, or resulting in autonomy from such regulators, cause an advancing wave of tumour cells and a receding wave of normal cells. By contrast, mutations affecting the production of a mitotic regulator cause a slow localized increase in the numbers of both normal and mutant cells. We extend our model to investigate the possible effects of an immune response to cancer by including a first order removal of mutant cells. When this removal rate exceeds a critical value, the immune system can suppress tumour growth; we derive an expression for this critical value as a function of the parameters characterizing the mutation. Our results suggest that the effectiveness of the immune response after an oncogenic mutation depends crucially on the way in which the mutation affects the biochemical control of cell division.