The glucose distribution in 9L rat brain multicell tumor spheroids and its effect on cell necrosis

Asymmetric Growth of Tumor Spheroids in a Symmetric Environment

In this work, we studied the stability of radially symmetric growth in tumor spheroids using a reaction-diffusion model. In this model, nutrient concentration and internal pressure are local variables that implicitly relate the proliferation of cells to the growth of the tumor. The analytical solution of the governing model was presented in an orthonormal spherical harmonic basis. It was shown that the radially symmetric steady-state solution to the growth of tumor spheroids, under symmetric growth conditions, was unstable with respect to small asymmetric perturbations. Such perturbations excited the asymmetric modes of growth, which could grow in time and change the spherical configuration of the tumor. The number of such modes and their rates of growth depended on parameters such as surface tension, external energy and the rate of nutrient consumption. This analysis indicated that the spherical configuration of tumor spheroids, even under experimentally controlled symmetric growth conditions, were naturally unstable. This was confirmed by a comparison between the shapes of in vitro human glioblastoma (hGB) spheroids and the configuration of the first few asymmetric modes predicted by the model.

Nm23-H1 activator phenylbutenoid dimer exerts cytotoxic effects on metastatic breast cancer cells by inducing mitochondrial dysfunction only under glucose starvation

Mitochondrial oxidative phosphorylation (OXPHOS) has become an attractive target in anti-cancer studies in recent years. In this study, we found that a small molecule phenylbutenoid dimer NMac1 (Nm23-H1 activator 1), (±)-trans-3-(3,4-dimethoxyphenyl)-4-[(E)-3,4-dimethoxystyryl]cyclohex-1-ene, a previously identified anti-metastatic agent, has novel anti-proliferative effect only under glucose starvation in metastatic breast cancer cells. NMac1 causes significant activation of AMPK by decreasing ATP synthesis, lowers mitochondrial membrane potential (MMP, ΔΨm), and inhibits oxygen consumption rate (OCR) under glucose starvation. These effects of NMac1 are provoked by a consequence of OXPHOS complex I inhibition. Through the structure–activity relationship (SAR) study of NMac1 derivatives, NMac24 was identified as the most effective compound in anti-proliferation. NMac1 and NMac24 effectively suppress cancer cell proliferation in 3D-spheroid in vivo-like models only under glucose starvation. These results suggest that NMac1 and NMac24 have the potential as anti-cancer agents having cytotoxic effects selectively in glucose restricted cells.

A superhydrophobic chip integrated with an array of medium reservoirs for long-term hanging drop spheroid culture

Hanging drop (HD) is one of the most popular methods used for forming three-dimensional (3D) cell spheroids. However, conventional hanging drop systems are only applicable for short-term spheroid culture due to their inconvenience in exchanging cell culture media. Here we present a medium-reservoir-integrated superhydrophobic (MRI-SH) chip for long-term HD spheroid cultures. The device consists of two main components: i) a patterned superhydrophobic (SH) surface containing an array of wettable spots which anchor arrays of droplets of cell suspension, and ii) an array of chambers that serve as medium reservoirs, both interconnected via an array of thru-holes. This configuration provides two distinct advantages over conventional HD configurations: i) the high wettability contrast of the SH pattern on the chip leads to the formation and adhesion of nearly spherical hanging droplets on its surface, which minimizes interactions between the liquid and the substrate; ii) the integrated chambers provide large volumes of medium to maintain longer culture durations. Using this device, spheroids of MHCC97H cells were successfully formed, and the cultured spheroids could maintain high viability for up to 30 days and exhibited enhanced spheroid morphology compared to those cultured in the conventional HD systems. STATEMENT OF SIGNIFICANCE: This paper presents a medium-reservoir-integrated superhydrophobic hanging drop (HD) platform for the long-term culture of spheroids with enhanced morphology. By monolithically integrating medium reservoirs and a patterned SH surface into a single device, this HD platform can not only produce high-quality spheroids, but also permit them to sustain high viability for up to 30 days without the need for tedious medium replenishment. We believe that such a platform will be valuable in a wide range of biological or biomedical applications, including tissue engineering, regenerative medicine, and drug discovery.

Cell – extracellular matrix interaction in glioma growth. In silico model

The study aims to investigate the role of viscoelastic interactions between cells and extracellular matrix (ECM) in avascular tumor growth. Computer simulations of glioma multicellular tumor spheroid (MTS) growth are being carried out for various conditions. The calculations are based on a continuous model, which simulates oxygen transport into MTS; transitions between three cell phenotypes, cell transport, conditioned by hydrostatic forces in cell–ECM composite system, cell motility and cell adhesion. Visco-elastic cell aggregation and elastic ECM scaffold represent two compressible constituents of the composite. Cell–ECM interactions form a Transition Layer on the spheroid surface, where mechanical characteristics of tumor undergo rapid transition. This layer facilitates tumor progression to a great extent. The study demonstrates strong effects of ECM stiffness, mechanical deformations of the matrix and cell–cell adhesion on tumor progression. The simulations show in particular that at certain, rather high degrees of matrix stiffness a formation of distant multicellular clusters takes place, while at further increase of ECM stiffness subtumors do not form. The model also illustrates to what extent mere mechanical properties of cell–ECM system may contribute into variations of glioma invasion scenarios.

Collective invasion of glioma cells through OCT1 signalling and interaction with reactive astrocytes after surgery

Glioblastoma multiforme (GBM) is the most aggressive form of brain cancer with a short median survival time. GBM is characterized by the hallmarks of aggressive proliferation and cellular infiltration of normal brain tissue. miR-451 and its downstream molecules are known to play a pivotal role in regulation of the balance of proliferation and aggressive invasion in response to metabolic stress in the tumour microenvironment (TME). Surgery-induced transition in reactive astrocyte populations can play a significant role in tumour dynamics. In this work, we develop a multi-scale mathematical model of miR-451-LKB1-AMPK-OCT1-mTOR pathway signalling and individual cell dynamics of the tumour and reactive astrocytes after surgery. We show how the effects of fluctuating glucose on tumour cells need to be reprogrammed by taking into account the recent history of glucose variations and an AMPK/miR-451 reciprocal feedback loop. The model shows how variations in glucose availability significantly affect the activity of signalling molecules and, in turn, lead to critical cell migration. The model also predicts that microsurgery of a primary tumour induces phenotypical changes in reactive astrocytes and stem cell-like astrocytes promoting tumour cell proliferation and migration by Cxcl5. Finally, we investigated a new anti-tumour strategy by Cxcl5-targeting drugs. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Role of extracellular matrix and microenvironment in regulation of tumor growth and LAR-mediated invasion in glioblastoma

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 cues in the microenvironment. Recent studies have shown that miR-451 regulates downstream molecules including AMPK/CAB39/MARK and mTOR to determine the balance between rapid proliferation and invasion in response to metabolic stress in the harsh tumor microenvironment. Surgical removal of the 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 complex process of cell proliferation and invasion and its response to conventional treatment, we propose a mathematical model that analyzes the intracellular dynamics of the miR-451-AMPK- mTOR-cell cycle signaling pathway within a cell. The model identifies a key mechanism underlying the molecular switches between proliferative phase and migratory phase in response to metabolic stress in response to fluctuating glucose levels. We show how up- or down-regulation of components in these pathways affects the key cellular decision to infiltrate or proliferate in a complex microenvironment in the absence and presence of time delays and stochastic noise. Glycosylated chondroitin sulfate proteoglycans (CSPGs), a major component of the extracellular matrix (ECM) in the brain, contribute to the physical structure of the local brain microenvironment but also induce or inhibit glioma invasion by regulating the dynamics of the CSPG receptor LAR as well as the spatiotemporal activation status of resident astrocytes and tumor-associated microglia. Using a multi-scale mathematical model, we investigate a CSPG-induced switch between invasive and non-invasive tumors through the coordination of ECM-cell adhesion and dynamic changes in stromal cells. We show that the CSPG-rich microenvironment is associated with non-invasive tumor lesions through LAR-CSGAG binding while the absence of glycosylated CSPGs induce the critical glioma invasion. We illustrate how high molecular weight CSPGs can regulate the exodus of local reactive astrocytes from the main tumor lesion, leading to encapsulation of non-invasive tumor and inhibition of tumor invasion. These different CSPG conditions also change the spatial profiles of ramified and activated microglia. The complex distribution of CSPGs in the tumor microenvironment can determine the nonlinear invasion behaviors of glioma cells, which suggests the need for careful therapeutic strategies.

The role of spatial variations of abiotic factors in mediating intratumour phenotypic heterogeneity

We present here a space- and phenotype-structured model of selection dynamics between cancer cells within a solid tumour. In the framework of this model, we combine formal analyses with numerical simulations to investigate in silico the role played by the spatial distribution of abiotic components of the tumour microenvironment in mediating phenotypic selection of cancer cells. Numerical simulations are performed both on the 3D geometry of an in silico multicellular tumour spheroid and on the 3D geometry of an in vivo human hepatic tumour, which was imaged using computerised tomography. The results obtained show that inhomogeneities in the spatial distribution of oxygen, currently observed in solid tumours, can promote the creation of distinct local niches and lead to the selection of different phenotypic variants within the same tumour. This process fosters the emergence of stable phenotypic heterogeneity and supports the presence of hypoxic cells resistant to cytotoxic therapy prior to treatment. Our theoretical results demonstrate the importance of integrating spatial data with ecological principles when evaluating the therapeutic response of solid tumours to cytotoxic therapy.

A multiscale agent-based framework integrated with a constraint-based metabolic network model of cancer for simulating avascular tumor growth

The integration of an agent-based framework with a constraint-based metabolic network model of cancer for simulating avascular tumor growth.

Targeting Mitochondrial Function to Treat Quiescent Tumor Cells in Solid Tumors

The disorganized nature of tumor vasculature results in the generation of microenvironments characterized by nutrient starvation, hypoxia and accumulation of acidic metabolites. Tumor cell populations in such areas are often slowly proliferating and thus refractory to chemotherapeutical drugs that are dependent on an active cell cycle. There is an urgent need for alternative therapeutic interventions that circumvent growth dependency. The screening of drug libraries using multicellular tumor spheroids (MCTS) or glucose-starved tumor cells has led to the identification of several compounds with promising therapeutic potential and that display activity on quiescent tumor cells. Interestingly, a common theme of these drug screens is the recurrent identification of agents that affect mitochondrial function. Such data suggest that, contrary to the classical Warburg view, tumor cells in nutritionally-compromised microenvironments are dependent on mitochondrial function for energy metabolism and survival. These findings suggest that mitochondria may represent an “Achilles heel” for the survival of slowly-proliferating tumor cells and suggest strategies for the development of therapy to target these cell populations.

Induction of mitochondrial dysfunction as a strategy for targeting tumour cells in metabolically compromised microenvironments

Abnormal vascularization of solid tumours results in the development of microenvironments deprived of oxygen and nutrients that harbour slowly growing and metabolically stressed cells. Such cells display enhanced resistance to standard chemotherapeutic agents and repopulate tumours after therapy. Here we identify the small molecule VLX600 as a drug that is preferentially active against quiescent cells in colon cancer 3-D microtissues. The anticancer activity is associated with reduced mitochondrial respiration, leading to bioenergetic catastrophe and tumour cell death. VLX600 shows enhanced cytotoxic activity under conditions of nutrient starvation. Importantly, VLX600 displays tumour growth inhibition in vivo. Our findings suggest that tumour cells in metabolically compromised microenvironments have a limited ability to respond to decreased mitochondrial function, and suggest a strategy for targeting the quiescent populations of tumour cells for improved cancer treatment.

Quiescent sub-populations of cells in tumours are resistant to traditional chemotherapeutics and are responsible for tumour recurrence. Here, Zhang et al. identify a compound that kills quiescent tumour cells in solid tumour tissue by inducing mitochondrial dysfunction.

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 anomalous diffusion of a tumor invading with different surrounding tissues

We simulated the invasion of a proliferating, diffusing tumor within different surrounding tissue conditions using a hybrid mathematical model. The in silico invasion of a tumor was addressed systematically for the first time within the framework of a generalized diffusion theory. Our results reveal that a tumor not only migrates using typical Fickian diffusion, but also migrates more generally using subdiffusion, superdiffusion, and even ballistic diffusion, with increasing mobility of the tumor cell when haptotaxis and chemotaxis toward the host tissue surrounding the proliferative tumor are involved. Five functional terms were included in the hybrid model and their effects on a tumor's invasion were investigated quantitatively: haptotaxis toward the extracellular matrix tissue that is degraded by matrix metalloproteinases; chemotaxis toward nutrients; cell-cell adhesion; the proliferation of the tumor; and the immune response toward the tumor. Haptotaxis and chemotaxis, which are initiated by extracellular matrix and nutrient supply (i.e., glucose) respectively, as well as cell-cell adhesions all drastically affect a tumor's diffusion mode when a tumor invades its surrounding host tissue and proliferates. We verified the in silico invasive behavior of a tumor by analyzing experimental data gathered from the in vitro culturing of different tumor cells and clinical imaging observations that used the same approach as was used to process the simulation data. The different migration modes of a tumor suggested by the simulations generally conform to the results observed in cell cultures and in clinical imaging. Our study not only discloses some migration modes of a tumor that proliferates and invades under different host tissues conditions, but also provides a heuristic method to characterize the invasion of a tumor in clinical medical imaging analysis.

High performance conducting polymer nanofiber biosensors for detection of biomolecules

Sensitive detection and selective determination of the physiologically important chemicals involved in brain function have drawn much attention for the diagnosis and treatment of brain diseases and neurological disorders. This paper reports a novel method for fabrication of enzyme entrapped-conducting polymer nanofibers that offer higher sensitivity and increased lifetime compared to glucose sensors that are based on conducting polymer films.

Metabolic scaling in solid tumours

Tumour metabolism is an outstanding topic of cancer research, as it determines the growth rate and the global activity of tumours. Recently, by combining the diffusion of oxygen, nutrients, and metabolites in the extracellular environment, and the internal motions that mix live and dead cells, we derived a growth law of solid tumours which is linked to parameters at the cellular level1. Here we use this growth law to obtain a metabolic scaling law for solid tumours, which is obeyed by tumours of different histotypes both in vitro and in vivo, and we display its relation with the fractal dimension of the distribution of live cells in the tumour mass. The scaling behaviour is related to measurable parameters, with potential applications in the clinical practice.

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

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

A numerical model of EMT6/Ro spheroid dynamics under irradiation: calibration and estimation of the underlying irradiation-induced cell survival probability

We present extensions to our quasi-2D cellular automata spheroid model that add a cellular kinetics module together with an irradiation and repair module. Significantly, our approach is not based on the Linear Quadratic (LQ) model, instead, we propose a simple two-parameter, algorithmic model which captures the essential biological features of irradiation-induced cell death, repair and associated cell cycle delays. This approach allows us to estimate directly the underlying irradiation-induced cell survival probability. We present the calibration of this extended model both with and without the application of single irradiation doses to the commonly studied (in vitro) EMT6/Ro (mammary carcinoma) cell line. A comparison of the estimated underlying cell survival probability with the in vitro survival probability data confirms the expected differences in the measures.

Hypoxia inducible factors-mediated inhibition of cancer by GM-CSF: a mathematical model

Under hypoxia, tumor cells, and tumor-associated macrophages produce VEGF (vascular endothelial growth factor), a signaling molecule that induces angiogenesis. The same macrophages, when treated with GM-CSF (granulocyte/macrophage colony-stimulating factor), produce sVEGFR-1 (soluble VEGF receptor-1), a soluble protein that binds with VEGF and inactivates its function. The production of VEGF by macrophages is regulated by HIF-1α (hypoxia inducible factor-1α), and the production of sVEGFR-1 is mediated by HIF-2α. Recent experiments measured the effect of inhibiting tumor growth by GM-CSF treatment in mice with HIF-1α-deficient or HIF-2α-deficient macrophages. In the present paper, we represent these experiments by a mathematical model based on a system of partial differential equations. We show that the model simulations agree with the above experiments. The model can then be used to suggest strategies for inhibiting tumor growth. For example, the model qualitatively predicts the extent to which GM-CSF treatment in combination with a small molecule inhibitor that stabilizes HIF-2α will reduce tumor volume and angiogenesis.

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.

Necrotic core in EMT6/Ro tumour spheroids: Is it caused by an ATP deficit?

Although commonly related to nutrient deprivation, the cause of the formation of the necrotic core in the multicellular tumour spheroids is still a controversial issue. We propose a simple model for the cell ATP production that assumes glucose and lactate as the only fuel substrates, and describes the main reactions occurring in the glycolytic and the oxidative pathways. Under the key assumption that cell death occurs when ATP production falls to a critical level, we formulate a multiscale model that integrates the energy metabolism at the cellular level with the diffusive transport of the metabolites in the spheroid mass. The model has been tested by predicting the measurements of the necrotic radius obtained by Freyer and Sutherland (1986a) in EMT6/Ro spheroids under different concentrations of glucose and oxygen in the culture medium. The results appear to be in agreement with the hypothesis that necrosis is caused by ATP deficit.

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.

Three-dimensional modeling of transport of nutrients for multicellular tumor spheroid culture in a microchannel

The growth dynamics of avascular tumors in a microchannel bioreactor is investigated. A three-dimensional flow and nutrient transport model, incorporating the multicellular tumor spheroid (MTS) growth model, has been developed to study the influence of nutrients (oxygen and glucose) supply and distribution on the MTS growth. Numerical simulations based on the EMT6/Ro tumor cells show that the continuous-flow perfusion is more efficient to deliver nutrients to the MTS than the diffusion-only static culture. It is further demonstrated that as long as there is bulk flow, the growth of a single tumor spheroid at the early stage is insensitive to the flow velocity and the channel size. For multiple tumor spheroids in the same microchannel, however, increasing the perfusion velocity can improve the nutrient environment for the disadvantageous downstream tumor spheroid. The flow shear stress exerting on the MTSs in the current microchannel bioreactor is estimated to be far below the critical value to affect the MTS growth, which means that there is still much room for increasing perfusion velocity to satisfy the higher nutrient requirement by the growing tumor spheroids.

A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment

Glioblastoma, the most malignant form of brain cancer, is responsible for 23% of primary brain tumors and has extremely poor outcome. Confounding the clinical management of glioblastomas is the extreme local invasiveness of these cancer cells. The mechanisms that govern invasion are poorly understood. To gain insight into glioblastoma invasion, we conducted experiments on the patterns of growth and dispersion of U87 glioblastoma tumor spheroids in a three-dimensional collagen gel. We studied two different cell lines, one with a mutation to the EGFR (U87DeltaEGFR) that is associated with increased malignancy, and one with an endogenous (wild-type) receptor (U87WT). We developed a continuum mathematical model of the dispersion behaviors with the aim of identifying and characterizing discrete cellular mechanisms underlying invasive cell motility. The mathematical model quantitatively reproduces the experimental data, and indicates that the U87WT invasive cells have a stronger directional motility bias away from the spheroid center as well as a faster rate of cell shedding compared to the U87DeltaEGFR cells. The model suggests that differences in tumor cell dispersion may be due to differences in the chemical factors produced by cells, differences in how the two cell lines remodel the gel, or different cell-cell adhesion characteristics.

Evolution of oxygen and glucose concentration profiles in a tissue-mimetic culture system of embryonic stem cells

A tissue-mimetic culture system (TMCS) in which cells are sandwiched between two glass slides provides an ideal microenvironment for studying the effects of oxygen and nutrient gradients on cells in culture. A mathematical model was utilized to predict the time course of the development of oxygen and glucose concentration gradients within the TMCS. Oxygen and glucose consumption rates of mouse embryonic stem cells were measured as parameters for the model. The model predicts oxygen and glucose concentration profiles directly using a single experimentally controlled variable, the seeding density of cells within the system. The model predicts that the time required for the gradients to reach steady state is inversely related to the cell density, and the penetration depth of the gradients into the TMCS is inversely related to the square root of the cell density. Experimental oxygen concentration measurements were performed at a cell density of 9.1 x 10(6) cells cm(-3), and the gradient was found to develop to a steady-state profile within 20 min and penetrate approximately 2 mm into the TMCS, consistent with the theoretical predictions. This model and the TMCS provide useful tools for investigating the effect of the metabolic microenvironment on cells in culture.

Dynamics and pattern formation in invasive tumor growth

We study the in vitro dynamics of the malignant brain tumor glioblastoma multiforme. The growing tumor consists of a dense proliferating zone and an outer less dense invasive region. Experiments with different types of cells show qualitatively different behavior: one cell line invades in a spherically symmetric manner, but another gives rise to branches. We formulate a model for this sort of growth using two coupled reaction-diffusion equations for the cell and nutrient concentrations. When the ratio of the nutrient and cell diffusion coefficients exceeds some critical value, the plane propagating front becomes unstable with respect to transversal perturbations. The instability threshold and the full phase-plane diagram in the parameter space are determined. The results are in a qualitative agreement with experimental findings for the two types of cells.

Tumor growth instability and the onset of invasion

Motivated by experimental observations, we develop a mathematical model of chemotactically directed tumor growth. We present an analytical study of the model as well as a numerical one. The mathematical analysis shows that: (i) tumor cell proliferation by itself cannot generate the invasive branching behavior observed experimentally, (ii) heterotype chemotaxis provides an instability mechanism that leads to the onset of tumor invasion, and (iii) homotype chemotaxis does not provide such an instability mechanism but enhances the mean speed of the tumor surface. The numerical results not only support the assumptions needed to perform the mathematical analysis but they also provide evidence of (i), (ii), and (iii). Finally, both the analytical study and the numerical work agree with the experimental phenomena.

Growth patterns of microscopic brain tumors

Highly malignant brain tumors such as glioblastoma multiforme form complex growth patterns in vitro in which invasive cells organize in tenuous branches. Here, we formulate a chemotaxis model for this sort of growth. A key element controlling the pattern is homotype attraction, i.e., the tendency for invasive cells to follow pathways previously explored. We investigate this in two ways: we show that there is an intrinsic instability in the model, which leads to branch formation. We also give a discrete description for the expansion of the invasive zone, and a continuum model for the nutrient supply. The results indicate that both strong heterotype chemotaxis and strong homotype chemoattraction are required for branch formation within the invasive zone. Our model thus can give a way to assess the importance of the various processes, and a way to explore and analyze transitions between different growth regimes.

Effect of ploidy, recruitment, environmental factors, and tamoxifen treatment on the expression of sigma-2 receptors in proliferating and quiescent tumour cells

Recently, we demonstrated that sigma-2 receptors may have the potential to be a biomarker of tumour cell proliferation (Mach et al (1997) Cancer Res 57: 156-161). If sigma-2 receptors were a biomarker of tumour cell proliferation, they would be amenable to detection by non-invasive imaging procedures, thus eliminating many of the problems associated with the flow cytometric measures of tumour cell proliferation presently used in the clinic. To be a good biomarker of tumour cell proliferation, the expression of sigma-2 receptors must be essentially independent of many of the biological, physiological, and/or environmental properties that are found in solid tumours. In the investigation reported here, the mouse mammary adenocarcinoma lines, 66 (diploid) and 67 (aneuploid), 9L rat brain tumour cells, and MCF-7 human breast tumour cells were used to study the extent and kinetics of expression of sigma-2 receptors in proliferative (P) and quiescent (Q) tumour cells as a function of species, cell type, ploidy, pH, nutrient depletion, metabolic state, recruitment from the Q-cell compartment to the P-cell compartment, and treatment with tamoxifen. In these experiments, the expression of sigma-2 receptors solely reflected the proliferative status of the tumour cells. None of the biological, physiological, or environmental properties that were investigated had a measurable effect on the expression of sigma-2 receptors in these model systems. Consequently, these data suggest that the proliferative status of tumours and normal tissues can be non-invasively assessed using radiolabelled ligands that selectively bind sigma-2 receptors.

Inhibition of T cell proliferation by macrophage tryptophan catabolism

We have recently shown that expression of the enzyme indoleamine 2, 3-dioxygenase (IDO) during murine pregnancy is required to prevent rejection of the allogeneic fetus by maternal T cells. In addition to their role in pregnancy, IDO-expressing cells are widely distributed in primary and secondary lymphoid organs. Here we show that monocytes that have differentiated under the influence of macrophage colony-stimulating factor acquire the ability to suppress T cell proliferation in vitro via rapid and selective degradation of tryptophan by IDO. IDO was induced in macrophages by a synergistic combination of the T cell-derived signals IFN-gamma and CD40-ligand. Inhibition of IDO with the 1-methyl analogue of tryptophan prevented macrophage-mediated suppression. Purified T cells activated under tryptophan-deficient conditions were able to synthesize protein, enter the cell cycle, and progress normally through the initial stages of G1, including upregulation of IL-2 receptor and synthesis of IL-2. However, in the absence of tryptophan, cell cycle progression halted at a mid-G1 arrest point. Restoration of tryptophan to arrested cells was not sufficient to allow further cell cycle progression nor was costimulation via CD28. T cells could exit the arrested state only if a second round of T cell receptor signaling was provided in the presence of tryptophan. These data reveal a novel mechanism by which antigen-presenting cells can regulate T cell activation via tryptophan catabolism. We speculate that expression of IDO by certain antigen presenting cells in vivo allows them to suppress unwanted T cell responses.

Levels of selected growth factors in viable and necrotic regions of xenografted HCT-8 human colon tumours

Xenografted tumours were produced in nude mice by injection of HCT-8 human colon tumour cells. At average volumes of about 750 mm3, animals were injected with fast green vital dye, and 20 min later, tumours were excised and dissected into viable (stained) and necrotic portions (unstained). Viable and necrotic regions were then examined for cell yields, colony forming efficiencies, and levels of basic fibroblast growth factor (FGF-2), transforming growth factors-beta 1 and -alpha (TGF-beta 1, TGF-alpha), platelet derived growth factor (PDGF), and vascular endothelial growth factor (VEGF) using enzyme-linked immunoassay (ELISA) procedures. Levels in the viable and necrotic regions were compared to levels in unseparated tumours. The average extent of necrosis in HCT-8 tumours of this size was 64%. The data for cell yields, colony forming efficiencies FGF-2, VEGF, TGF-beta 1 and TGF-alpha indicated that values determined in the unseparated tumours could be understood on the basis of the weighted average between viable and necrotic tissue, with the higher values occurring in the viable tissue. Low levels of FGF-2 and VEGF were found in the necrotic portions of the tumour while no measurable levels of TGF-beta 1 and TGF-alpha could be determined. PDGF levels were, however, equivalent in both the viable and necrotic regions indicating that necrotic tissue could be an important reservoir for this growth factor.

Cell aggregation in a Chinese hamster ovary cell microcarrier culture affects the expression rate and N-linked glycosylation of recombinant mouse placental lactogen-1

A microcarrier culture of Chinese hamster ovary (CHO) cells, expressing the N-glycosylated recombinant protein mouse placental lactogen I (mPL-I), was found to form large cellular aggregates (400 to 600 microns in diameter). There was increased accumulation of lower molecular sized mPL-I glycoforms in cultures containing the large cellular aggregates at pH 7.3, but not at pH 7.6. Specific rates of mPL-I expression were found in the cultures with cellular aggregates at both pH values (7.3 and 7.6). These findings are interpreted in the light of our earlier studies that showed that extracellular pH and elevated ammonia concentrations affect both the glycosylation and the expression rates of mouse placental lactogen I.

Glucose diffusion coefficients determined from concentration profiles in EMT6 tumor spheroids incubated in radioactively labeled L-glucose

A method for performing and evaluating autoradiography of diffusible 14C labeled substances in multicellular tumor spheroids is presented that allows one to obtain a diffusion coefficient of the substance investigated from each individual spheroid. Application of the method with 14C labeled L-glucose resulted in a glucose diffusion coefficient of 5 x 10(-6) cm2/s. It also revealed problems of the method at very short incubation times of about 10 s or less. These problems are most likely caused by the large penetration depth of beta particles irradiated by 14C labels (as compared to 3H labels) which tends to transform steep 14C concentration gradients into much more shallow optical density gradients during exposure. This transformation can be corrected for by deconvolution of the recorded optical density distributions. Basic data and mathematical tools necessary for the process of deconvolution are presently being developed. It is planned to use this method for determining diffusion coefficients of other substances of interest. One such group of substances are the metabolic waste products, most importantly lactate. Another group consists of larger molecules, e.g. peptides and comprises the various growth factors important in tumor biology. Since for members of this latter group little is known about their velocity of penetration into tissue, model calculations may be applied to predict a range of incubation times suitable for determining diffusion coefficients. Moreover, the algorithms for data analysis will have to be modified to allow for receptor binding of the substance under study.(ABSTRACT TRUNCATED AT 250 WORDS)

Bioreductive metabolism of AF-2[2-(2-furyl)-3-(5-nitro-2-furyl)acrylamide] combined with 2-nitroimidazoles. Implications for use as hypoxic cell markers

Metabolism of misonidazole under hypoxic conditions depletes the parent drug and causes about 4% of the reduced-drug-products to form adducts with cellular macromolecules (binding), and this process has been used to detect hypoxia in cells and tissues. The nitrofuran, AF-2 [2-(2-furyl)-3-(5-nitro-2-furyl)acrylamide] has been shown to increase both the metabolic depletion of misonidazole and its binding. In the present study, factors which might affect this process have been examined, in an in vitro system, to test the hypothesis that metabolic depletion of misonidazole could limit its ability to diffuse freely to the hypoxic cell population. Drastic reductions in glucose concentrations from their normal value of 5-10 mM to less than 0.5 mM had no significant effect on the metabolism of either misonidazole or AF-2. Similarly, glucose concentration did not influence the binding of misonidazole, even when concentrations of both oxygen (extreme hypoxia) and glucose were near zero--a very toxic biochemical environment. Similarly, the metabolism of the nitroheterocyclics had no effect on glucose consumption. The bioreductive depletion of misonidazole in extreme hypoxia appeared to be independent of drug concentration between 25 and 100 microM: this nearly zero-order rate of drug metabolism prevented the possibility of working at constant drug concentration. AF-2 exacerbated this effect by greatly enhancing the metabolic depletion of misonidazole. AF-2 was found to increase both the metabolic depletion and binding of misonidazole by the same factor. An unexpected finding was that metabolism of etanidazole, a 2-nitroimidazole closely related to misonidazole, was not enhanced by AF-2. Micromolar amounts of oxygen inhibited the reductive activation of AF-2, and also the interaction between AF-2 and misonidazole. Our results suggest that metabolic depletion of nitroheterocyclics could influence their ability to diffuse adequately to hypoxic tissues, particularly at the low drug concentrations that have been used to measure tissue hypoxia in vivo.

Variations in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration, and extracellular pH

Tumors and multicellular tumor spheroids can develop gradients in oxygen concentration, glucose concentration, and extracellular pH as they grow. In order to calculate these gradients and assess their impact on tumor growth, it is necessary to quantify the effect of these variables on tumor cell metabolism and growth. In this work, the oxygen consumption rates, glucose consumption rates, and growth rates of EMT6/Ro mouse mammary tumor cells were measured at a variety of oxygen concentrations, glucose concentrations, and extracellular pH levels. At an extracellular pH of 7.25, the oxygen consumption rate of EMT6/Ro cells increased by nearly a factor of 2 as the glucose concentration was decreased from 5.5 mM to 0.4 mM. This effect of glucose concentration on oxygen consumption rate, however, was slight at an extracellular pH of 6.95 and disappeared completely at an extracellular pH of 6.60. The glucose consumption rate of EMT6/Ro cells increased by roughly 40% when the oxygen concentration was reduced from 0.21 mM to 0.023 mM and decreased by roughly 60% when the extracellular pH was decreased from 7.25 to 6.95. The growth rate of EMT6/Ro cells decreased with decreasing oxygen concentration and extracellular pH; however, severe conditions were required to stop cell growth (0.0082 mM oxygen and an extracellular pH of 6.60). Empirical correlations were developed from these data to express EMT6/Ro cell growth rates, oxygen consumption rates, and glucose consumption rates, as functions of oxygen concentration, glucose concentration, and extracellular pH. These empirical correlations make it possible to mathematically model the gradients in oxygen concentration, glucose concentration, and extracellular pH in EMT6/Ro multicellular spheroids by solution of the diffusion/reaction equations. Computations such as these, along with oxygen and pH microelectrode measurements in EMT6/Ro multicellular spheroids, indicated that nutrient concentration and pH levels in the inner regions of spheroids were low enough to cause significant changes in nutrient consumption rates and cell growth rates. However, pH and oxygen concentrations measured or calculated in EMT6/Ro spheroids where quiescent cells have been observed were not low enough to cause the cessation of cell growth, indicating that the observed quiescence must have been due to factors other than acidic pH, oxygen depletion, or glucose depletion.

Mechanisms behind the resistance of spheroids to photodynamic treatment: a flow cytometry study

The influence of cell heterogeneity on response to photodynamic treatment (PDT) has been investigated using the human colon adenocarcinoma line WiDr, grown as spheroids and exposed to hematoporphyrin derivative. The spheroids show a marked spheroid size-dependent resistance to PDT. Using a flow cytometer, cell sub-populations have been separated, on the basis of drug fluorescence, from single cell suspensions prepared from 500 microm diameter spheroids. Cells low in fluorescence have been shown to be resistant to PDT, have a smaller median cell volume, and be enhanced in G1-type cells. These cells also show reduced low density lipoprotein uptake. The results suggest that spheroid size-dependent resistance to PDT is related to a decreasing growth fraction with increasing spheroid size. Heterogeneity of drug uptake could be a potential limitation to clinical PDT.

Mathematical modelling of microenvironment and growth in EMT6/Ro multicellular tumour spheroids

In order to determine the role of micromilieu in tumour spheroid growth, a mathematical model was developed to predict EMT6/Ro spheroid growth and microenvironment based upon numerical solution of the diffusion/reaction equation for oxygen, glucose, lactate ion, carbon dioxide, bicarbonate ion, chlorine ion and hydrogen ion along with the equation of electroneutrality. This model takes into account the effects of oxygen concentration, glucose concentration and extracellular pH on cell growth and metabolism. Since independent measurements of EMT6/Ro single cell growth and metabolic rates, spheroid diffusion constants, and spinner flask mass transfer coefficients are available, model predictions using these parameters were compared with published data on EMT6/Ro spheroid growth and micro-environment. The model predictions of reduced spheroid growth due to reduced cell growth rates and cell shedding fit experimental spheroid growth data below 700 microns, but overestimated the spheroid growth rate at larger diameters. Predicted viable rim thicknesses based on predicted near zero glucose concentrations fit published viable rim thickness data for 1000 microns spheroids grown at medium glucose concentrations of 5.5 mM or less. However, the model did not accurately predict the onset of necrosis. Moreover, the model could not predict the observed decreases in oxygen and glucose metabolism seen in spheroids with time, nor could it predict the observed growth plateau. This suggests that other unknown factors, such as inhibitors or cell-cell contact effects, must also be important in affecting spheroid growth and cellular metabolism.

Energy metabolism, pH changes, and lactate production in RIF-1 tumors following intratumoral injection of glucose

The metabolic consequences of increased glucose availability were examined in subcutaneous RIF-1 tumors in vivo, using 13C and 31P NMR spectroscopy. Significant increases in the levels of nucleotide triphosphates and phosphocreatine relative to low energy phosphates and in tumor pH were observed within 30 min following injection of 1 g/kg of glucose directly into the tumor. These changes did not occur following an equivalent intratumoral dose of the non-metabolizable sugar alcohol, mannitol. When [1-13C]-glucose was administered, [3-13C]-lactate and [3-13C]-alanine were the only labeled metabolites detected in the in vivo 13C NMR spectra during the period of bioenergetic improvement. Biochemical analysis revealed a substantial increase in tumor and plasma glucose concentration, but no increase in either tumor or plasma lactate, consistent with the absence of acidosis. Evaluation of the distribution of glucose in the tumor by quantitative autoradiography of [1-14C]-2-deoxyglucose administered with the glucose indicated that, on average, 7 mM of the added glucose distributed over the entire tumor within 10 min. The significant improvement in overall metabolic status of the tumors following glucose administration is attributed to the existence of substrate limited regions within the tumor.

Effects of changes in oxygen tension, pH, and glucose concentration on the response to CCNU of EMT6 mouse tumor monolayer cells and multicellular spheroids

We have studied the effect of individually changing medium glucose content, pH and oxygen tension upon the response to CCNU (1-(2-chloroethyl)3-cyclohexyl-1-nitrosourea) of EMT6/Ca/VJAC cells grown as early plateau phase monolayer cultures or small (200 microns diameter) spheroids. The effect of changing all three factors together has also been studied in the spheroid model. All the changes in medium conditions (except for 4 hr hypoxia) were maintained for 24 hr prior to drug exposure. Plating efficiency (PE) of monolayer cells was decreased by reduced medium pH (below 6.5) or oxygen tension while no change in PE was brought about by reduced medium glucose content. In small spheroids reduction in PE caused by low pH was similar to that seen in monolayer, there was again no effect of reduced glucose, and the effect of hypoxia was clearly less than in monolayer. Combination treatment of spheroids (pH 6.5, 120 mg/l glucose and hypoxia) reduced the PE of spheroid cells to 50% of control. Reducing medium glucose content from 920 to 0 mg/l, or oxygen tension from 20% to near zero (for either 4 or 24 hr) reduced the sensitivity of monolayer cells to CCNU. A similar pattern was seen for reducing medium pH from 7.2 to 6.1 during the 24 hr pre-incubation period and 1 hr drug exposure period. A reverse trend was, however, seen if medium pH during the drug exposure period was maintained at 7.2 following reduced pH pre-incubation. Reduced sensitivity to CCNU was seen for cells within small spheroids pre-incubated in medium at low pH (for both schedules) or under hypoxia (for either 4 or 24 hr) whereas reduced medium glucose content appeared to have no such effect. Cells in small spheroids after 24 hr combination treatment were also less sensitive to CCNU than cells from control spheroids.

Cell and environment interactions in tumor microregions: the multicell spheroid model

Abnormal vascularization of malignant tumors is associated with the development of microregions of heterogeneous cells and environments. Experimental models such as multicell spheroids and a variety of new techniques are being used to determine the characteristics of these microregions and to study the interactions of the cells and microenvironments. The special cellular microecology of tumors influences responsiveness to therapeutic agents and has implications for future directions in cancer research.

Joint oxygen-glucose deprivation as the cause of necrosis in a tumor analog

The sandwich system was recently developed as an in vitro tumor analog. Like spheroids, sandwiches are organized, multicellular systems in which the interplay between diffusion and consumption leads to the formation of spatial gradients; a necrotic center and a viable cell border subsequently develop. Using sandwiches of the 9L and V79 cell lines, the effects of oxygen and glucose deprivation on the onset and formation of necrosis were investigated. The data indicate that in sandwiches necrosis is a result of a shortage of both substances. Complementary cell monolayer experiments to determine a number of consumption parameters were performed. On the basis of the data, we propose a joint oxygen-glucose deprivation model for V79 cell necrosis. It is assumed a cell dies when oxygen deprivation in conjunction with glucose deprivation lowers the cell's ATP production rate below a critical value. Interactions of the concentrations and consumptions of oxygen and glucose are analyzed theoretically; concentration profiles are obtained by numerically solving coupled non-linear integral equations arising from the diffusion equation. The predicted viable border widths are in good agreement with the observed values.

Therapeutic drug monitoring in oncology. Problems and potential in antineoplastic therapy

Therapeutic drug monitoring is now widely used in many areas of medicine. With its proliferation has come an understanding of the clinical situations in which it is likely to be of value. Factors that can limit the usefulness of therapeutic drug monitoring and situations where it is less likely to be of benefit have also been identified. At present, the routine use of therapeutic drug monitoring in antineoplastic therapy is limited to measurement of plasma methotrexate concentrations after high-dose methotrexate therapy. The lack of a more widespread application of therapeutic drug monitoring in oncology has been due to deficiencies in knowledge about the clinical pharmacology of antineoplastic agents and to factors specific to the chemotherapy of neoplasms. These factors include the broad heterogeneity of malignant neoplasms, the complexities of the drug-tumour interaction, difficulties in assessment of this interaction and the use of combinations of antineoplastic agents with cumulative efficacies and toxicities. Despite these problems, there are many areas in antineoplastic therapy where the use of therapeutic drug monitoring could prove of benefit. The prevention of the chronic pulmonary toxicity of bleomycin, the assessment of the bioavailability of oral chemotherapy, and monitoring drug disposition in the presence of hepatic or renal dysfunction are just some of the potential applications. If recent emphasis on dose as a critical factor in the success of cancer chemotherapy is substantiated, then the need to apply therapeutic drug monitoring within oncology will become more pressing.

Nutrient modification of proliferation and radiation response in EMT6/Ro spheroids

The effects of external nutrients on the growth and radiation response of EMT6/Ro spheroids were studied by maintaining spheroids in media with different concentrations of glucose, amino acids, and vitamins. Compared to spheroids grown in normal glucose concentration (5.5 mM), spheroids grown in higher glucose media (24.8 mM), demonstrated no difference in initial volume doubling time, clonogenicity, number of proliferating cells, or cell cycle distributions. However, histology sections revealed that, spheroids grown in higher glucose concentration had a thicker viable rim than spheroids grown in normal glucose media. Two-step acridine orange staining and dual parameter flow cytometric analysis, in addition to continuous [3H]-thymidine labeling techniques, showed that spheroids grown in higher glucose had 2 to 3 times the fraction of quiescent cells, when compared to normal glucose spheroids. When irradiated in ice to reoxygenate, the Do's were similar in the normal and the higher glucose spheroids, but the Dq's were reduced in the higher glucose spheroids in the presence of increased amino acids and vitamins. When irradiated in air at 37 degrees C, spheroids grown in the higher glucose media were more sensitive (decreased Do), and had a smaller hypoxic fraction than when grown in normal glucose media. For spheroids grown in the same glucose concentrations but increased concentrations of amino acids and vitamins, there was generally an increased Do under all irradiation conditions. Some of these differences in radiation sensitivity could be correlated to differences in cellular glutathione levels of these spheroid cells.