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.     

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.     

Role of Constitutive Behavior and Tumor-Host Mechanical Interactions in the State of Stress and Growth of Solid Tumors

Mechanical forces play a crucial role in tumor patho-physiology. Compression of cancer cells inhibits their proliferation rate, induces apoptosis and enhances their invasive and metastatic potential. Additionally, compression of intratumor blood vessels reduces the supply of oxygen, nutrients and drugs, affecting tumor progression and treatment. Despite the great importance of the mechanical microenvironment to the pathology of cancer, there are limited studies for the constitutive modeling and the mechanical properties of tumors and on how these parameters affect tumor growth. Also, the contribution of the host tissue to the growth and state of stress of the tumor remains unclear. To this end, we performed unconfined compression experiments in two tumor types and found that the experimental stress-strain response is better fitted to an exponential constitutive equation compared to the widely used neo-Hookean and Blatz-Ko models. Subsequently, we incorporated the constitutive equations along with the corresponding values of the mechanical properties - calculated by the fit - to a biomechanical model of tumor growth. Interestingly, we found that the evolution of stress and the growth rate of the tumor are independent from the selection of the constitutive equation, but depend strongly on the mechanical interactions with the surrounding host tissue. Particularly, model predictions - in agreement with experimental studies - suggest that the stiffness of solid tumors should exceed a critical value compared with that of the surrounding tissue in order to be able to displace the tissue and grow in size. With the use of the model, we estimated this critical value to be on the order of 1.5. Our results suggest that the direct effect of solid stress on tumor growth involves not only the inhibitory effect of stress on cancer cell proliferation and the induction of apoptosis, but also the resistance of the surrounding tissue to tumor expansion.     

Stress-mediated progression of solid tumors: effect of mechanical stress on tissue oxygenation,cancer cell proliferation,and drug delivery

Oxygen supply plays a central role in cancer cell proliferation. While vascular density increases at the early stages of carcinogenesis, mechanical solid stresses developed during growth compress tumor blood vessels and, thus, drastically reduce not only the supply of oxygen, but also the delivery of drugs at inner tumor regions. Among other effects, hypoxia and reduced drug delivery compromise the efficacy of radiation and chemo/nanotherapy, respectively. In the present study, we developed a mathematical model of tumor growth to investigate the interconnections among tumor oxygenation that supports cancer cell proliferation, the heterogeneous accumulation of mechanical stresses owing to tumor growth, the non-uniform compression of intratumoral blood vessels due to the mechanical stresses, and the insufficient delivery of oxygen and therapeutic agents because of vessel compression. We found that the high vascular density and increased cancer cell proliferation often observed in the periphery compared to the interior of a tumor can be attributed to heterogeneous solid stress accumulation. Highly vascularized peripheral regions are also associated with greater oxygenation compared with the compressed, less vascularized inner regions. We also modeled the delivery of drugs of two distinct sizes, namely chemotherapy and nanomedicine. Model predictions suggest that drug delivery is affected negatively by vessel compression independently of the size of the therapeutic agent. Finally, we demonstrated the applicability of our model to actual geometries, employing a breast tumor model derived from MR images.     

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.     

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.     

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.     

Compressive Stress Inhibits Proliferation in Tumor Spheroids through a Volume Limitation

In most instances, the growth of solid tumors occurs in constrained environments and requires a competition for space. A mechanical crosstalk can arise from this competition. In this article, we dissect the biomechanical sequence caused by a controlled compressive stress on multicellular spheroids (MCSs) used as a tumor model system. On timescales of minutes, we show that a compressive stress causes a reduction of the MCS volume, linked to a reduction of the cell volume in the core of the MCS. On timescales of hours, we observe a reversible induction of the proliferation inhibitor, p27^Kip1, from the center to the periphery of the spheroid. On timescales of days, we observe that cells are blocked in the cell cycle at the late G1 checkpoint, the restriction point. We show that the effect of pressure on the proliferation can be antagonized by silencing p27^Kip1. Finally, we quantify a clear correlation between the pressure-induced volume change and the growth rate of the spheroid. The compression-induced proliferation arrest that we studied is conserved for five cell lines, and is completely reversible. It demonstrates a generic crosstalk between mechanical stresses and the key players of cell cycle regulation. Our results suggest a role of volume change in the sensitivity to pressure, and that p27^Kip1 is strongly influenced by this change.     

Compressive Stress Inhibits Proliferation in Tumor Spheroids through a Volume Limitation

In most instances, the growth of solid tumors occurs in constrained environments and requires a competition for space. A mechanical crosstalk can arise from this competition. In this article, we dissect the biomechanical sequence caused by a controlled compressive stress on multicellular spheroids (MCSs) used as a tumor model system. On timescales of minutes, we show that a compressive stress causes a reduction of the MCS volume, linked to a reduction of the cell volume in the core of the MCS. On timescales of hours, we observe a reversible induction of the proliferation inhibitor, p27^Kip1, from the center to the periphery of the spheroid. On timescales of days, we observe that cells are blocked in the cell cycle at the late G1 checkpoint, the restriction point. We show that the effect of pressure on the proliferation can be antagonized by silencing p27^Kip1. Finally, we quantify a clear correlation between the pressure-induced volume change and the growth rate of the spheroid. The compression-induced proliferation arrest that we studied is conserved for five cell lines, and is completely reversible. It demonstrates a generic crosstalk between mechanical stresses and the key players of cell cycle regulation. Our results suggest a role of volume change in the sensitivity to pressure, and that p27^Kip1 is strongly influenced by this change.     

Modeling mechanical inhomogeneities in small populations of proliferating monolayers and spheroids

Understanding the mechanical behavior of multicellular monolayers and spheroids is fundamental to tissue culture, organism development, and the early stages of tumor growth. Proliferating cells in monolayers and spheroids experience mechanical forces as they grow and divide and local inhomogeneities in the mechanical microenvironment can cause individual cells within the multicellular system to grow and divide at different rates. This differential growth, combined with cell division and reorganization, leads to residual stress. Multiple different modeling approaches have been taken to understand and predict the residual stresses that arise in growing multicellular systems, particularly tumor spheroids. Here, we show that by using a mechanically robust agent-based model constructed with the peridynamic framework, we gain a better understanding of residual stresses in multicellular systems as they grow from a single cell. In particular, we focus on small populations of cells (1–100 s) where population behavior is highly stochastic and prior investigation has been limited. We compare the average strain energy density of cells in monolayers and spheroids using different growth and division rules and find that, on average, cells in spheroids have a higher strain energy density than cells in monolayers. We also find that cells in the interior of a growing spheroid are, on average, in compression. Finally, we demonstrate the importance of accounting for stochastic fluctuations in the mechanical environment, particularly when the cellular response to mechanical cues is nonlinear. The results presented here serve as a starting point for both further investigation with agent-based models, and for the incorporation of major findings from agent-based models into continuum scale models when explicit representation of individual cells is not computationally feasible.     

Imaging- and Flow Cytometry-based Analysis of Cell Position and the Cell Cycle in 3D Melanoma Spheroids

Three-dimensional (3D) tumor spheroids are utilized in cancer research as a more accurate model of the in vivo tumor microenvironment, compared to traditional two-dimensional (2D) cell culture. The spheroid model is able to mimic the effects of cell-cell interaction, hypoxia and nutrient deprivation, and drug penetration. One characteristic of this model is the development of a necrotic core, surrounded by a ring of G1 arrested cells, with proliferating cells on the outer layers of the spheroid. Of interest in the cancer field is how different regions of the spheroid respond to drug therapies as well as genetic or environmental manipulation. We describe here the use of the fluorescence ubiquitination cell cycle indicator (FUCCI) system along with cytometry and image analysis using commercial software to characterize the cell cycle status of cells with respect to their position inside melanoma spheroids. These methods may be used to track changes in cell cycle status, gene/protein expression or cell viability in different sub-regions of tumor spheroids over time and under different conditions.     

Computational challenges of tumor spheroid modeling

The speed and the versatility of today's computers open up new opportunities to simulate complex biological systems. Here we review a computational approach recently proposed by us to model large tumor cell populations and spheroids, and we put forward general considerations that apply to any fine-grained numerical model of tumors. We discuss ways to bypass computational limitations and discuss our incremental approach, where each step is validated by experimental observations on a quantitative basis. We present a few results on the growth of tumor cells in closed and open environments and of tumor spheroids. This study suggests new ways to explore the initial growth phase of solid tumors and to optimize antitumor treatments.     

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.     

Fibroblast EXT1-Levels Influence Tumor Cell Proliferation and Migration in Composite Spheroids

Background

Stromal fibroblasts are important determinants of tumor cell behavior. They act to condition the tumor microenvironment, influence tumor growth, support tumor angiogenesis and affect tumor metastasis. Heparan sulfate proteoglycans, present both on tumor and stromal cells, interact with a large number of ligands including growth factors, their receptors, and structural components of the extracellular matrix. Being ubiquitously expressed in the tumor microenvironment heparan sulfate proteoglycans are candidates for playing central roles in tumor-stroma interactions. The objective of this work was to investigate the role of heparan sulfate expressed by stromal fibroblasts in modulating the growth of tumor cells and in controlling the interstitial fluid pressure in a 3-D model.

Methodology/Principal Findings

We generated spheroids composed of fibroblasts alone, or composite spheroids, composed of fibroblasts and tumor cells. Here we show that stromal fibroblasts with a mutation in the heparan sulfate elongating enzyme Ext1 and thus a low heparan sulfate content, formed composite fibroblast/tumor cell spheroids with a significant lower interstitial fluid pressure than corresponding wild-type fibroblast/tumor cell composite spheroids. Furthermore, immunohistochemistry of composite spheroids revealed that the cells segregated, so that after 6 days in culture, the wild-type fibroblasts formed an inner core and the tumor cells an outer layer of cells. For composite spheroids containing Ext1-mutated fibroblasts this segregation was less obvious, indicating impaired cell migration. Analysis of tumor cells expressing the firefly luciferase gene revealed that the changes in tumor cell migration in mutant fibroblast/tumor cell composite spheroids coincided with a lower proliferation rate.

Conclusions/Significance

This is the first demonstration that stromal Ext1-levels modulate tumor cell proliferation and affect the interstitial fluid pressure in a 3-D spheroid model. Learning how structural changes in stromal heparan sulfate influence tumor cells is essential for our understanding how non-malignant cells of the tumor microenvironment influence tumor cell progression.     

Purinergic signaling as potential target of thiamethoxam-induced neurotoxicity using silver catfish (<Emphasis Type="Italic">Rhamdia quelen</Emphasis>) as experimental model

Resveratrol is a polyphenolic compound in many edible foods including grapes, peanuts, and berries. Several studies have revealed the beneficial effects of resveratrol against various diseases such as heart disease, diabetes, obesity, neurological disorders, and cancer. A recent study showed that resveratrol inhibits the proliferation of HCT116 human colorectal cancer cells in three-dimensional culture (3DC) via induction of luminal apoptosis in HCT116 cell spheroids. In this study, we showed that a novel compound, caffeic acid-adducted resveratrol, has a stronger inhibitory effect on the growth of HCT116 cell spheroids in 3DC than resveratrol. It showed almost the same inhibitory efficacy as 5-fluorouracil, a conventional anticancer drug. We further showed that the resveratrol derivative did not affect the growth of HKe3 cell spheroids derived from HCT116 cells by disruption of the activating mutant KRAS gene. These results suggest that the resveratrol derivative inhibits the growth of HCT116 cell spheroids via inhibition of an oncogenic KRAS-mediated signaling pathway.     

Cancer spheroids derived exosomes reveal more molecular features relevant to progressed cancer

Cancer cell spheroids have been shown to be more physiologically relevant to native tumor tissue than monolayer 2D culture cells. Due to enhanced intercellular communications among cells in spheroids, spheroid secreted exosomes which account for transcellular transportation should exceed those from 2D cell culture and may display a different expression pattern of miRNA or protein. To test this, we employed a widely used pancreatic cancer cell line, PANC-1, to create 3D spheroids and compared exosomes generated by both 2D cell culture and 3D PANC-1 spheroids. We further measured and compared exosomal miRNA and GPC-1 protein expression with qRT-PCR and enzyme-linked immunosorbent assay, respectively. It showed that PANC-1 cells cultured in 3D spheroids can produce significantly more exosomes than PANC-1 2D cells and exosomal miRNA and GPC-1 expression derived from spheroids show more features relevant to the progression of pancreatic cancer. These findings point to the potential importance of using spheroids as in vitro model to study cancer development and progression.     

Individual-based and continuum models of growing cell populations: a comparison

In this paper we compare two alternative theoretical approaches for simulating the growth of cell aggregates in vitro: individual cell (agent)-based models and continuum models. We show by a quantitative analysis of both a biophysical agent-based and a continuum mechanical model that for densely packed aggregates the expansion of the cell population is dominated by cell proliferation controlled by mechanical stress. The biophysical agent-based model introduced earlier (Drasdo and Hoehme in Phys Biol 2:133-147, 2005) approximates each cell as an isotropic, homogeneous, elastic, spherical object parameterised by measurable biophysical and cell-biological quantities and has been shown by comparison to experimental findings to explain the growth patterns of dense monolayers and multicellular spheroids. Both models exhibit the same growth kinetics, with initial exponential growth of the population size and aggregate diameter followed by linear growth of the diameter and power-law growth of the cell population size. Very sparse monolayers can be explained by a very small or absent cell-cell adhesion and large random cell migration. In this case the expansion speed is not controlled by mechanical stress but by random cell migration and can be modelled by the Fisher-Kolmogorov-Petrovskii-Piskounov (FKPP) reaction-diffusion equation. The growth kinetics differs from that of densely packed aggregates in that the initial spread, as quantified by the radius of gyration, is diffusive. Since simulations of the lattice-free agent-based model in the case of very large random migration are too long to be practical, lattice-based cellular automaton (CA) models have to be used for a quantitative analysis of sparse monolayers. Analysis of these dense monolayers leads to the identification of a critical parameter of the CA model so that eventually a hierarchy of three model types (a detailed biophysical lattice-free model, a rule-based cellular automaton and a continuum approach) emerge which yield the same growth pattern for dense and sparse cell aggregates.     

Immune and nonimmune mechanisms mediate the mental stress-induced tumor growth in a xenograft model of breast cancer

Excess mental stress may harm health, and even accelerate cancer initiation and progression. One fourth of breast cancer patients suffer mental stress including anxiety, sadness, or depression, which negatively affect prognosis and survival. However, the regulatory mechanism is yet to be determined. Herein, we applied unpredictable stress stimuli to the breast tumor-bearing mice to establish a xenograft model of breast cancer suffering mental stress, followed by behavioral tests, tumor growth tracking, immune analysis, miRNA screening, and tumor cell proliferation analysis as well. As a result, increased stress hormone levels in serum, decreased percentage of T and NK cells in both blood and tumor samples and accelerated tumor growth in vivo were observed in the mice exposed to mental stress. Promoted cell proliferation was observed in both primary tumor cells derived from the stressed mice and 4T1 breast cancer cells treated with stress hormone corticosterone. In addition, a subset of miRNAs including miR-326, 346, 493, 595, 615, and 665 were identified through a miRNA screening with downregulation in tumors of the stressed mice. CCND1 was identified as a common target gene of miR-346 and miR-493, the top two most significantly downregulated miRNAs by stress exposure. The stress-miRNA-CCND1 signaling regulation of the tumor cell proliferation was further validated in 4T1 cells treated with corticosterone in vitro. GO terms and KEGG pathways analyses on the target genes of miR-346 and miR-493 revealed their involvement in the regulation of human cancer and neuron system, indicating the importance of non-coding genome in mediating the mental stress-induced cancer regulation. In conclusion, this study not only explored immune and nonimmune mechanisms through which mental stress exposure contributes to tumor growth in breast cancer, but also suggested a new therapeutic strategy for cancer patients suffering mental stress.Subject terms: Breast cancer, Disease model, miRNAs     

A mathematical model of the stress induced during avascular tumour growth

In this paper a mathematical model is developed to describe the effect of nonuniform growth on the mechanical stress experienced by cells within an avascular tumour. The constitutive law combines the stress-strain relation of linear elasticity with a growth term that is derived by analogy with thermal expansion. To accommodate the continuous nature of the growth process, the law relates the rate of change of the stress tensor to the rate of change of the strain (rather than relating the stress to the strain directly). By studying three model problems which differ in detail, certain characteristic features are identified. First, cells near the tumour boundary, where nutrient levels and cell proliferation rates are high, are under compression. By contrast, cells towards the centre of the tumour, where nutrient levels are low and cell death dominant, are under tension. The implications of these results and possible model developments are also discussed. Received: 15 November 1999 / Published online: 5 May 2000