Modeling adaptive drug resistance of colorectal cancer and therapeutic interventions with tumor spheroids

Drug resistance is a major barrier against successful treatments of cancer patients. Various intrinsic mechanisms and adaptive responses of tumor cells to cancer drugs often lead to failure of treatments and tumor relapse. Understanding mechanisms of cancer drug resistance is critical to develop effective treatments with sustained anti-tumor effects. Three-dimensional cultures of cancer cells known as spheroids present a biologically relevant model of avascular tumors and have been increasingly incorporated in tumor biology and cancer drug discovery studies. In this review, we discuss several recent studies from our group that utilized colorectal tumor spheroids to investigate responses of cancer cells to cytotoxic and molecularly targeted drugs and uncover mechanisms of drug resistance. We highlight our findings from both short-term, one-time treatments and long-term, cyclic treatments of tumor spheroids and discuss mechanisms of adaptation of cancer cells to the treatments. Guided by mechanisms of resistance, we demonstrate the feasibility of designing specific drug combinations to effectively block growth and resistance of cancer cells in spheroid cultures. Finally, we conclude with our perspectives on the utility of three-dimensional tumor models and their shortcomings and advantages for phenotypic and mechanistic studies of cancer drug resistance.     

A single-cell-based model of tumor growth in vitro: monolayers and spheroids

To what extent the growth dynamics of tumors is controlled by nutrients, biomechanical forces and other factors at different stages and in different environments is still largely unknown. Here we present a biophysical model to study the spatio-temporal growth dynamics of two-dimensional tumor monolayers and three-dimensional tumor spheroids as a complementary tool to in vitro experiments. Within our model each cell is represented as an individual object and parametrized by cell-biophysical and cell-kinetic parameters that can all be experimentally determined. Hence our modeling strategy allows us to study which mechanisms on the microscopic level of individual cells may affect the macroscopic properties of a growing tumor. We find the qualitative growth kinetics and patterns at early growth stages to be remarkably robust. Quantitative comparisons between computer simulations using our model and published experimental observations on monolayer cultures suggest a biomechanically-mediated form of growth inhibition during the experimentally observed transition from exponential to sub-exponential growth at sufficiently large tumor sizes. Our simulations show that the same transition during the growth of avascular tumor spheroids can be explained largely by the same mechanism. Glucose (or oxygen) depletion seems to determine mainly the size of the necrotic core but not the size of the tumor. We explore the consequences of the suggested biomechanical form of contact inhibition, in order to permit an experimental test of our model. Based on our findings we propose a phenomenological growth law in early expansion phases in which specific biological small-scale processes are subsumed in a small number of effective parameters.     

Dynamical Interactions between Multiple Cancers

Multiple tumors in a patient have the possibility to interact with each other, through the competition for new blood supply which is required for growth and progression (angiogenesis). The multiple tumors can be independent, multiple primary cancers. Alternatively, they can be metastases which originate from one primary tumor. This paper uses mathematical models to investigate such dynamical interactions between multiple cancers. We start with a model which describes the growth of a single angiogenic tumor, and then generalize this model to include multiple tumors which compete for circulating endothelial progenitor cells in order to build new blood vessels. We explore under which conditions multiple tumors can coexist, and when one tumor can exclude other tumors from growing. Based on this framework, we discuss the circumstances under which independent multiple primary tumors can arise. We further discuss the inefficiency of metastatic cells to grow successfully, and suggest an explanation for the occurrence of multiple metastases with an unknown primary cancer.     

Stress generation,relaxation and size control in confined tumor growth

Experiments on tumor spheroids have shown that compressive stress from their environment can reversibly decrease tumor expansion rates and final sizes. Stress release experiments show that nonuniform anisotropic elastic stresses can be distributed throughout. The elastic stresses are maintained by structural proteins and adhesive molecules, and can be actively relaxed by a variety of biophysical processes. In this paper, we present a new continuum model to investigate how the growth-induced elastic stresses and active stress relaxation, in conjunction with cell size control feedback machinery, regulate the cell density and stress distributions within growing tumors as well as the tumor sizes in the presence of external physical confinement and gradients of growth-promoting chemical fields. We introduce an adaptive reference map that relates the current position with the reference position but adapts to the current position in the Eulerian frame (lab coordinates) via relaxation. This type of stress relaxation is similar to but simpler than the classical Maxwell model of viscoelasticity in its formulation. By fitting the model to experimental data from two independent studies of tumor spheroid growth and their cell density distributions, treating the tumors as incompressible, neo-Hookean elastic materials, we find that the rates of stress relaxation of tumor tissues can be comparable to volumetric growth rates. Our study provides insight on how the biophysical properties of the tumor and host microenvironment, mechanical feedback control and diffusion-limited differential growth act in concert to regulate spatial patterns of stress and growth. When the tumor is stiffer than the host, our model predicts tumors are more able to change their size and mechanical state autonomously, which may help to explain why increased tumor stiffness is an established hallmark of malignant tumors.     

Thymoquinone reduces mouse colon tumor cell invasion and inhibits tumor growth in murine colon cancer models

We have shown that thymoquinone (TQ) is a potent antitumor agent in human colorectal cancer cells. In this study, we evaluated TQ's therapeutic potential in two different mice colon cancer models [1,2-dimethyl hydrazine (DMH) and xenografts]. We also examined TQ effects on the growth of C26 mouse colorectal carcinoma spheroids and assessed tumor invasion in vitro. Mice were treated with saline, TQ, DMH, or combinations once per week for 30 weeks and the multiplicity, size and distribution of aberrant crypt foci (ACF) and tumors were determined at weeks 10, 20 and 30. TQ injected intraperitoneally (i.p.) significantly reduced the numbers and sizes of ACF at week 10; ACF numbers were reduced by 86%. Tumor multiplicity was reduced at week 20 from 17.8 in the DMH group to 4.2 in mice injected with TQ. This suppression was observed at week 30 and was long-term; tumors did not re-grow even when TQ injection was discontinued for 10 weeks. In a xenograft model of HCT116 colon cancer cells, TQ significantly (P < 0.05) delayed the growth of the tumor cells. Using a matrigel artificial basement membrane invasion assay, we demonstrated that sub-cyto-toxic doses of TQ (40 microM) decreased C26 cell invasion by 50% and suppressed growth in three-dimensional spheroids. Apoptotic signs seen morphologically were increased significantly in TQ-treated spheroids. TUNEL staining of xenografts and immunostaining for caspase 3 cleavage in DMH tumors confirmed increased apoptosis in mouse tumors in response to TQ. These data should encourage further in vivo testing and support the potential use of TQ as a therapeutic agent in human colorectal cancer.     

Mechanical Stress Impairs Mitosis Progression in Multi-Cellular Tumor Spheroids

Growing solid tumors are subjected to mechanical stress that influences their growth rate and development. However, little is known about its effects on tumor cell biology. To explore this issue, we investigated the impact of mechanical confinement on cell proliferation in MultiCellular Tumor Spheroids (MCTS), a 3D culture model that recapitulates the microenvironment, proliferative gradient, and cell-cell interactions of a tumor. Dedicated polydimethylsiloxane (PDMS) microdevices were designed to spatially restrict MCTS growth. In this confined environment, spheroids are likely to experience mechanical stress as indicated by their modified cell morphology and density and by their relaxation upon removal from the microdevice. We show that the proliferation gradient within mechanically confined spheroids is different in comparison to MCTS grown in suspension. Furthermore, we demonstrate that a population of cells within the body of mechanically confined MCTS is arrested at mitosis. Cell morphology analysis reveals that this mitotic arrest is not caused by impaired cell rounding, but rather that confinement negatively affects bipolar spindle assembly. All together these results suggest that mechanical stress induced by progressive confinement of growing spheroids could impair mitotic progression. This study paves the way to future research to better understand the tumor cell response to mechanical cues similar to those encountered during in vivo tumor development.     

The process of macrophage migration promotes matrix metalloproteinase-independent invasion by tumor cells

Tumor-associated macrophages are known to amplify the malignant potential of tumors by secreting a variety of cytokines and proteases involved in tumor cell invasion and metastasis, but how these macrophages infiltrate tumors and whether the macrophage migration process facilitates tumor cell invasion remain poorly documented. To address these questions, we used cell spheroids of breast carcinoma SUM159PT cells as an in vitro model of solid tumors. We found that macrophages used both the mesenchymal mode requiring matrix metalloproteinases (MMPs) and the amoeboid migration mode to infiltrate tumor cell spheroids. Whereas individual SUM159PT cells invaded Matrigel using an MMP-dependent mesenchymal mode, when they were grown as spheroids, tumor cells were unable to invade the Matrigel surrounding spheroids. When spheroids were infiltrated or in contact with macrophages, tumor cell invasiveness was restored. It was dependent on the capacity of macrophages to remodel the matrix and migrate in an MMP-independent mesenchymal mode. This effect of macrophages was much reduced when spheroids were infiltrated by Matrigel migration-defective Hck(-/-) macrophages. In the presence of macrophages, SUM159PT migrated into Matrigel in the proximity of macrophages and switched from an MMP-dependent mesenchymal migration to an amoeboid mode resistant to protease inhibitors.Thus, in addition to the well-described paracrine loop between macrophages and tumor cells, macrophages can also contribute to the invasiveness of tumor cells by remodeling the extracellular matrix and by opening the way to exit the tumor and colonize the surrounding tissues in an MMP-dispensable manner.     

Human Neuroendocrine Tumor Cell Lines as a Three-Dimensional Model for the Study of Human Neuroendocrine Tumor Therapy

Neuroendocrine tumors (NETs) are rare tumors, with an incidence of two per 100, 000 individuals per year, and they account for 0.5% of all human malignancies.¹ Other than surgery for the minority of patients who present with localized disease, there is little or no survival benefit of systemic therapy. Therefore, there is a great need to better understand the biology of NETs, and in particular define new therapeutic targets for patients with nonresectable or metastatic neuroendocrine tumors. 3D cell culture is becoming a popular method for drug screening due to its relevance in modeling the in vivo tumor tissue organization and microenvironment.^2,3 The 3D multicellular spheroids could provide valuable information in a more timely and less expensive manner than directly proceeding from 2D cell culture experiments to animal (murine) models.To facilitate the discovery of new therapeutics for NET patients, we have developed an in vitro 3D multicellular spheroids model using the human NET cell lines. The NET cells are plated in a non-adhesive agarose-coated 24-well plate and incubated under physiological conditions (5% CO₂, 37 °C) with a very slow agitation for 16-24 hr after plating. The cells form multicellular spheroids starting on the 3^rd or 4^th day. The spheroids become more spherical by the 6^th day, at which point the drug treatments are initiated. The efficacy of the drug treatments on the NET spheroids is monitored based on the morphology, shape and size of the spheroids with a phase-contrast light microscope. The size of the spheroids is estimated automatically using a custom-developed MATLAB program based on an active contour algorithm. Further, we demonstrate a simple method to process the HistoGel embedding on these 3D spheroids, allowing the use of standard histological and immunohistochemical techniques. This is the first report on generating 3D spheroids using NET cell lines to examine the effect of therapeutic drugs. We have also performed histology on these 3D spheroids, and displayed an example of a single drug''s effect on growth and proliferation of the NET spheroids. Our results support that the NET spheroids are valuable for further studies of NET biology and drug development.     

An on-lattice agent-based Monte Carlo model simulating the growth kinetics of multicellular tumor spheroids

PurposeTo develop an on-lattice agent-based model describing the growth of multicellular tumor spheroids using simple Monte Carlo tools.MethodsCells are situated on the vertices of a cubic grid. Different cell states (proliferative, hypoxic or dead) and cell evolution rules, driven by 10 parameters, and the effects of the culture medium are included. About twenty spheroids of MCF-7 human breast cancer were cultivated and the experimental data were used for tuning the model parameters.ResultsSimulated spheroids showed adequate sizes of the necrotic nuclei and of the hypoxic and proliferative cell phases as a function of the growth time, mimicking the overall characteristics of the experimental spheroids. The relation between the radii of the necrotic nucleus and the whole spheroid obtained in the simulations was similar to the experimental one and the number of cells, as a function of the spheroid volume, was well reproduced. The statistical variability of the Monte Carlo model described the whole volume range observed for the experimental spheroids. Assuming that the model parameters vary within Gaussian distributions it was obtained a sample of spheroids that reproduced much better the experimental findings.ConclusionsThe model developed allows describing the growth of in vitro multicellular spheroids and the experimental variability can be well reproduced. Its flexibility permits to vary both the agents involved and the rules that govern the spheroid growth. More general situations, such as, e. g., tumor vascularization, radiotherapy effects on solid tumors, or the validity of the tumor growth mathematical models can be studied.     

A multiscale model for avascular tumor growth

The desire to understand tumor complexity has given rise to mathematical models to describe the tumor microenvironment. We present a new mathematical model for avascular tumor growth and development that spans three distinct scales. At the cellular level, a lattice Monte Carlo model describes cellular dynamics (proliferation, adhesion, and viability). At the subcellular level, a Boolean network regulates the expression of proteins that control the cell cycle. At the extracellular level, reaction-diffusion equations describe the chemical dynamics (nutrient, waste, growth promoter, and inhibitor concentrations). Data from experiments with multicellular spheroids were used to determine the parameters of the simulations. Starting with a single tumor cell, this model produces an avascular tumor that quantitatively mimics experimental measurements in multicellular spheroids. Based on the simulations, we predict: 1), the microenvironmental conditions required for tumor cell survival; and 2), growth promoters and inhibitors have diffusion coefficients in the range between 10(-6) and 10(-7) cm2/h, corresponding to molecules of size 80-90 kDa. Using the same parameters, the model also accurately predicts spheroid growth curves under different external nutrient supply conditions.     

A novel, patient-specific mathematical pathology approach for assessment of surgical volume: application to ductal carcinoma in situ of the breast

We introduce a novel "mathematical pathology" approach, founded on a biophysical model, to identify robust patient-specific predictors of tumor growth useful in clinical practice to improve the accuracy of diagnosis/prognosis and intervention. In accordance with biological observations, our model simulates the diffusion-limited in situ tumors with a relatively short phase of fast initial growth, followed by a prolonged slow-growth phase where tumor size is constrained primarily by the relative weight of cell mitosis and death. The former phase may only last for a few months, so that at the time of diagnosis, we may assume that most tumors will have entered the phase where their size is changing slowly. Based on this prediction, we hypothesize that the volume of breast with ducts affected by in situ tumors at the time of diagnosis will be closely approximated by a model-derived mathematical function based on the ratio of tumor cell proliferation-to-apoptosis indices and on the extent of diffusion of cell nutrients (diffusion penetration length), which can be measured from immunohistochemical and morphometric analysis of patient histopathology specimens without the need for multiple-time measurements. We tested this idea in a retrospective study of 17 patients by staining breast tumor specimens containing ductal carcinoma in situ for mitosis with Ki-67 and for apoptosis with cleaved caspase-3 and counting cells positive for each marker. We also determined diffusion penetration by measuring the thickness of viable rims of tumor cells within ducts. Using the ensuing ratios, we applied the model to determine a predicted surgical volume or tumor size. We then corroborated our hypothesis by comparing the predicted size of each tumor based on our model with the actual size of the pathological specimen after tumor excision (R2 = 0.74-0.88). In addition, for the 17 cases studied, both histological grade and mammography were not found to correlate with tumor size (R2 = 0.08-0.47). We conclude that our mathematical pathology approach yields a high degree of accuracy in predicting the size of tumors based on the mitotic/apoptotic index and on diffusion penetration. By obtaining these ratios at the time of initial biopsy, pathologists can employ our model to predict the size of the tumor and thereby inform surgeons how much tissue to remove (surgical volume). We discuss how results from the model have implications concerning the current debate on recommendations for screening mammography, while the model itself may contribute to better planning of breast conservation surgery.     

Exploring cancer stem cell niche directed tumor growth

The finding that only a sub-fraction of tumor cells, so called Cancer Stem Cells (CSC), is endowed with the capacity to initiate new tumors has important consequences for fundamental as well as clinical cancer research. Previously we established by computational modeling techniques that CSC driven tumor growth instigates infiltrative behavior, and perhaps most interesting, stimulates tumor cell heterogeneity. An important question that remains is to what extend CSC functions are intrinsically regulated or whether this capacity is orchestrated by the microenvironment, i.e. a putative CSC niche. Here we investigate how extrinsic regulation of CSC properties affects the characteristics of malignancies. We find that highly invasive growth in tumors dependent on a small subset of cells is not restricted to CSC-driven tumors, but is also observed in tumors where the CSC capacity of tumor cells is completely defined by the microenvironment. Importantly, also the high level of heterogeneity that was observed for CSC-driven tumors is preserved and partially even increased in malignancies with a microenvironmentally orchestrated CSC population. This indicates that invasive growth and high heterogeneity are fundamental properties of tumors fueled by a small population of tumor cells.     

Predicting the growth of glioblastoma multiforme spheroids using a multiphase porous media model

Tumor spheroids constitute an effective in vitro tool to investigate the avascular stage of tumor growth. These three-dimensional cell aggregates reproduce the nutrient and proliferation gradients found in the early stages of cancer and can be grown with a strict control of their environmental conditions. In the last years, new experimental techniques have been developed to determine the effect of mechanical stress on the growth of tumor spheroids. These studies report a reduction in cell proliferation as a function of increasingly applied stress on the surface of the spheroids. This work presents a specialization for tumor spheroid growth of a previous more general multiphase model. The equations of the model are derived in the framework of porous media theory, and constitutive relations for the mass transfer terms and the stress are formulated on the basis of experimental observations. A set of experiments is performed, investigating the growth of U-87MG spheroids both freely growing in the culture medium and subjected to an external mechanical pressure induced by a Dextran solution. The growth curves of the model are compared to the experimental data, with good agreement for both the experimental settings. A new mathematical law regulating the inhibitory effect of mechanical compression on cancer cell proliferation is presented at the end of the paper. This new law is validated against experimental data and provides better results compared to other expressions in the literature.     

Micro-Environmental Mechanical Stress Controls Tumor Spheroid Size and Morphology by Suppressing Proliferation and Inducing Apoptosis in Cancer Cells

Background

Compressive mechanical stress produced during growth in a confining matrix limits the size of tumor spheroids, but little is known about the dynamics of stress accumulation, how the stress affects cancer cell phenotype, or the molecular pathways involved.

Methodology/Principal Findings

We co-embedded single cancer cells with fluorescent micro-beads in agarose gels and, using confocal microscopy, recorded the 3D distribution of micro-beads surrounding growing spheroids. The change in micro-bead density was then converted to strain in the gel, from which we estimated the spatial distribution of compressive stress around the spheroids. We found a strong correlation between the peri-spheroid solid stress distribution and spheroid shape, a result of the suppression of cell proliferation and induction of apoptotic cell death in regions of high mechanical stress. By compressing spheroids consisting of cancer cells overexpressing anti-apoptotic genes, we demonstrate that mechanical stress-induced apoptosis occurs via the mitochondrial pathway.

Conclusions/Significance

Our results provide detailed, quantitative insight into the role of micro-environmental mechanical stress in tumor spheroid growth dynamics, and suggest how tumors grow in confined locations where the level of solid stress becomes high. An important implication is that apoptosis via the mitochondrial pathway, induced by compressive stress, may be involved in tumor dormancy, in which tumor growth is held in check by a balance of apoptosis and proliferation.     

Fibroblast α11β1 Integrin Regulates Tensional Homeostasis in Fibroblast/A549 Carcinoma Heterospheroids

We have previously shown that fibroblast expression of α11β1 integrin stimulates A549 carcinoma cell growth in a xenograft tumor model. To understand the molecular mechanisms whereby a collagen receptor on fibroblast can regulate tumor growth we have used a 3D heterospheroid system composed of A549 tumor cells and fibroblasts without (α11^+/+) or with a deletion (α11^-/-) in integrin α11 gene. Our data show that α11^-/-/A549 spheroids are larger than α11^+/+/A549 spheroids, and that A549 cell number, cell migration and cell invasion in a collagen I gel are decreased in α11^-/-/A549 spheroids. Gene expression profiling of differentially expressed genes in fibroblast/A549 spheroids identified CXCL5 as one molecule down-regulated in A549 cells in the absence of α11 on the fibroblasts. Blocking CXCL5 function with the CXCR2 inhibitor SB225002 reduced cell proliferation and cell migration of A549 cells within spheroids, demonstrating that the fibroblast integrin α11β1 in a 3D heterospheroid context affects carcinoma cell growth and invasion by stimulating autocrine secretion of CXCL5. We furthermore suggest that fibroblast α11β1 in fibroblast/A549 spheroids regulates interstitial fluid pressure by compacting the collagen matrix, in turn implying a role for stromal collagen receptors in regulating tensional hemostasis in tumors. In summary, blocking stromal α11β1 integrin function might thus be a stroma-targeted therapeutic strategy to increase the efficacy of chemotherapy.