Shedding of mitotic cells from the surface of multicell spheroids during growth

Mechanical feedback controls the emergence of dynamical memory in growing tissue monolayers

The growth of a tissue, which depends on cell–cell interactions and biologically relevant processes such as cell division and apoptosis, is regulated by a mechanical feedback mechanism. We account for these effects in a minimal two-dimensional model in order to investigate the consequences of mechanical feedback, which is controlled by a critical pressure, p c. A cell can only grow and divide if its pressure, due to interaction with its neighbors, is less than p c. Because temperature is not a relevant variable, the cell dynamics is driven by self-generated active forces (SGAFs) that arise due to cell division. We show that even in the absence of intercellular interactions, cells undergo diffusive behavior. The SGAF-driven diffusion is indistinguishable from the well-known dynamics of a free Brownian particle at a fixed finite temperature. When intercellular interactions are taken into account, we find persistent temporal correlations in the force–force autocorrelation function (FAF) that extends over a timescale of several cell division times. The time-dependence of the FAF reveals memory effects, which increases as p c increases. The observed non-Markovian effects emerge due to the interplay of cell division and mechanical feedback and are inherently a non-equilibrium phenomenon.

Agent-based model of multicellular tumor spheroid evolution including cell metabolism

Computational models aiming at the spatio-temporal description of cancer evolution are a suitable framework for testing biological hypotheses from experimental data, and generating new ones. Building on our recent work (J. Theor. Biol. 389, 146 (2016)) we develop a 3D agent-based model, capable of tracking hundreds of thousands of interacting cells, over time scales ranging from seconds to years. Cell dynamics is driven by a Monte Carlo solver, incorporating partial differential equations to describe chemical pathways and the activation/repression of "genes", leading to the up- or down-regulation of specific cell markers. Each cell-agent of different kind (stem, cancer, stromal etc.) runs through its cycle, undergoes division, can exit to a dormant, senescent, necrotic state, or apoptosis, according to the inputs from its systemic network. The basic network at this stage describes glucose/oxygen/ATP cycling, and can be readily extended to cancer-cell specific markers. Eventual accumulation of chemical/radiation damage to each cell's DNA is described by a Markov chain of internal states, and by a damage-repair network, whose evolution is linked to the cell systemic network. Aimed at a direct comparison with experiments of tumorsphere growth from stem cells, the present model will allow to quantitatively study the role of transcription factors involved in the reprogramming and variable radio-resistance of simulated cancer-stem cells, evolving in a realistic computer simulation of a growing multicellular tumorsphere.

A review of spatial computational models for multi-cellular systems, with regard to intestinal crypts and colorectal cancer development

Colon rectal cancers (CRC) are the result of sequences of mutations which lead the intestinal tissue to develop in a carcinoma following a "progression" of observable phenotypes. The actual modeling and simulation of the key biological structures involved in this process is of interest to biologists and physicians and, at the same time, it poses significant challenges from the mathematics and computer science viewpoints. In this report we give an overview of some mathematical models for cell sorting (a basic phenomenon that underlies several dynamical processes in an organism), intestinal crypt dynamics and related problems and open questions. In particular, major attention is devoted to the survey of so-called in-lattice (or grid) models and off-lattice (off-grid) models. The current work is the groundwork for future research on semi-automated hypotheses formation and testing about the behavior of the various actors taking part in the adenoma-carcinoma progression, from regulatory processes to cell-cell signaling pathways.

A review of spatial computational models for multi-cellular systems, with regard to intestinal crypts and colorectal cancer development

Colon rectal cancers (CRC) are the result of sequences of mutations which lead the intestinal tissue to develop in a carcinoma following a "progression" of observable phenotypes. The actual modeling and simulation of the key biological structures involved in this process is of interest to biologists and physicians and, at the same time, it poses significant challenges from the mathematics and computer science viewpoints. In this report we give an overview of some mathematical models for cell sorting (a basic phenomenon that underlies several dynamical processes in an organism), intestinal crypt dynamics and related problems and open questions. In particular, major attention is devoted to the survey of so-called in-lattice (or grid) models and off-lattice (off-grid) models. The current work is the groundwork for future research on semi-automated hypotheses formation and testing about the behavior of the various actors taking part in the adenoma-carcinoma progression, from regulatory processes to cell-cell signaling pathways.

Some implications of Scale Relativity theory in avascular stages of growth of solid tumors in the presence of an immune system response

We present a traveling-wave analysis of a reduced mathematical model describing the growth of a solid tumor in the presence of an immune system response in the framework of Scale Relativity theory. Attention is focused upon the attack of tumor cells by tumor-infiltrating cytotoxic lymphocytes (TICLs), in a small multicellular tumor, without necrosis and at some stage prior to (tumor-induced) angiogenesis. For a particular choice of parameters, the underlying system of partial differential equations is able to simulate the well-documented phenomenon of cancer dormancy and propagation of a perturbation in the tumor cell concentration by cnoidal modes, by depicting spatially heterogeneous tumor cell distributions that are characterized by a relatively small total number of tumor cells. This behavior is consistent with several immunomorphological investigations. Moreover, the alteration of certain parameters of the model is enough to induce soliton like modes and soliton packets into the system, which in turn result in tumor invasion in the form of a standard traveling wave. In the same framework of Scale Relativity theory, a very important feature of malignant tumors also results, that even in avascular stages they might propagate and invade healthy tissues, by means of a diffusion on a Newtonian fluid.

Tumour angiogenesis: the gap between theory and experiments

A common experimental technique for viewing in vivo angiogenesis utilises tumours implanted into a test animal cornea. The cornea is avascular but the tumour promotes vascularisation from the limbus and the new blood vessels can be readily observed through the transparent cornea. Many of the early mathematical models for tumour angiogenesis used this scenario as their experimental template and as such assumed that there is a large gap, of the order of 2mm, between the tumour and neighbouring vasculature at the onset of angiogenesis. In this work we consider whether the assumption that there is a significant gap between the tumour and neighbouring vasculature is unique to intra-cornea tumour implants, or whether this characterises avascular tumour growth more generally. To do this we utilise a simple scaling argument, derive a multi-compartment model for tumour growth, and consider in vivo images. This analysis demonstrates that the corneal implant experiments and the corresponding mathematical models cannot generally be applied to a clinical setting.

Thymidine kinase 1 and thymidine phosphorylase expression in non-small-cell lung carcinoma in relation to angiogenesis and proliferation

The thymidine salvage pathway enzymes thymidine kinase 1 (TK1) and thymidine phosphorylase (TP) compete for thymidine as a substrate and catalyze opposing synthetic and catabolic reactions that have been implicated in the control of proliferation and angiogenesis, respectively. We investigated the relationship between the expression of TK1 and TP as they relate to proliferation (Ki-67 labeling index) and angiogenesis (Chalkley count of CD31-stained blood vessels) in a series of 110 non-small-cell lung cancer (NSCLC) tumors from patients prospectively enrolled in an imaging trial. TK1 and TP exhibited similar patterns of immunohistochemical distribution, in that each was found in both the nucleus and the cytoplasm of tumor cells. Each enzyme exhibited a significant positive correlation between its levels of nuclear and cytoplasmic expression. A significant positive correlation between TK1 expression and the Ki-67 labeling index (r = 0.53, p<0.001) was observed. TP was significantly positively correlated with Chalkley scoring of CD31 staining in high vs low Chalkley scoring samples (mean TP staining of 115.8 vs 79.9 scoring units, p<0.001), respectively. We did not observe a substantial inverse correlation between the TP and TK1 expression levels in the nuclear compartment (r = -0.17, p=0.08). Tumor size was not found to be associated with TK1, TP, Ki-67, or Chalkley score. These findings provide additional evidence for the role of thymidine metabolism in the complex interaction of proliferation and angiogenesis in NSCLC.

Essential operating principles for tumor spheroid growth

BACKGROUND

Our objective was to discover in silico axioms that are plausible representations of the operating principles realized during characteristic growth of EMT6/Ro mouse mammary tumor spheroids in culture. To reach that objective we engineered and iteratively falsified an agent-based analogue of EMT6 spheroid growth. EMT6 spheroids display consistent and predictable growth characteristics, implying that individual cell behaviors are tightly controlled and regulated. An approach to understanding how individual cell behaviors contribute to system behaviors is to discover a set of principles that enable abstract agents to exhibit closely analogous behaviors using only information available in an agent's immediate environment. We listed key attributes of EMT6 spheroid growth, which became our behavioral targets. Included were the development of a necrotic core surrounded by quiescent and proliferating cells, and growth data at two distinct levels of nutrient.

RESULTS

We then created an analogue made up of quasi-autonomous software agents and an abstract environment in which they could operate. The system was designed so that upon execution it could mimic EMT6 cells forming spheroids in culture. Each agent used an identical set of axiomatic operating principles. In sequence, we used the list of targeted attributes to falsify and revise these axioms, until the analogue exhibited behaviors and attributes that were within prespecified ranges of those targeted, thereby achieving a level of validation.

CONCLUSION

The finalized analogue required nine axioms. We posit that the validated analogue's operating principles are reasonable representations of those utilized by EMT6/Ro cells during tumor spheroid development.

The role of extracellular matrix in glioma invasion: a cellular Potts model approach

In this work, a cellular Potts model based on the differential adhesion hypothesis is employed to analyze the relative importance of select cell-cell and cell-extracellular matrix (ECM) contacts in glioma invasion. To perform these simulations, three types of cells and two ECM components are included. The inclusion of explicit ECM with an inhomogeneous fibrous component and a homogeneously dispersed afibrous component allows exploration of the importance of relative energies of cell-cell and cell-ECM contacts in a variety of environments relevant to in vitro and in vivo experimental investigations of glioma invasion. Simulations performed here focus chiefly on reproducing findings of in vitro experiments on glioma spheroids embedded in collagen I gels. For a given range and set ordering of energies associated with key cell-cell and cell-ECM interactions, our model qualitatively reproduces the dispersed glioma invasion patterns found for most glioma cell lines embedded as spheroids in collagen I gels of moderate concentration. In our model, we find that invasion is maximized at intermediate collagen concentrations, as occurs experimentally. This effect is seen more strongly in model gels composed of short collagen fibers than in those composed of long fibers, which retain significant connectivity even at low density. Additional simulations in aligned model matrices further elucidate how matrix structure dictates invasive patterns. Finally, simulations that allow invading cells to both dissolve and deposit ECM components demonstrate how Q-Potts models may be elaborated to allow active cell alteration of their surroundings. The model employed here provides a quantitative framework with which to bound the relative values of cell-cell and cell-ECM interactions and investigate how varying the magnitude and type of these interactions, as well as ECM structure, could potentially curtail glioma invasion.

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.

Continuum versus discrete model: a comparison for multicellular tumour spheroids

We study multicellular tumour spheroids with a continuum model based on partial differential equations (PDEs). The model includes viable and necrotic cell densities, as well as oxygen and glucose concentrations. Viable cells consume nutrients and become necrotic below critical nutrient concentrations. Proliferation of viable cells is contact-inhibited if the total cellular density locally exceeds volume carrying capacity. The model is discussed under the assumption of spherical symmetry. Unknown model parameters are determined by simultaneously fitting the cell number to several experimental growth curves for different nutrient concentrations. The outcome of the PDE model is compared with an analogous off-lattice agent-based model for tumour growth. It turns out that the numerically more efficient PDE model suffices to explain the macroscopic growth data. As in the agent-based model, we find that the experimental growth curves are only reproduced when a necrotic core develops. However, evaluation of morphometric properties yields differences between the models and the experiment.

Proliferation and death in a binary environment: a stochastic model of cellular ecosystems

The activation, growth and death of animal cells are accompanied by changes in the chemical composition of the surrounding environment. Cells and their microscopic environment constitute therefore a cellular ecosystem whose time-evolution determines processes of interest for either biology (e.g. animal development) and medicine (e.g. tumor spreading, immune response). In this paper, we consider a general stochastic model of the interplay between cells and environmental cellular niches. Niches may be either favourable or unfavourable in sustaining cell activation, growth and death, the state of the niches depending on the state of the cells. Under the hypothesis of random coupling between the state of the environmental niche and the state of the cell, the rescaled model reduces to a set of four non-linear differential equations. The biological meaning of the model is studied and illustrated by fitting experimental data on the growth of multicellular tumor spheroids. A detailed analysis of the stochastic model, of its deterministic limit, and of normal fluctuations is provided.

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.

Multicellular tumor spheroid in an off-lattice Voronoi-Delaunay cell model

We study multicellular tumor spheroids by introducing a new three-dimensional agent-based Voronoi-Delaunay hybrid model. In this model, the cell shape varies from spherical in thin solution to convex polyhedral in dense tissues. The next neighbors of the cells are provided by a weighted Delaunay triangulation with on average linear computational complexity. The cellular interactions include direct elastic forces and cell-cell as well as cell-matrix adhesion. The spatiotemporal distribution of two nutrients--oxygen and glucose--is described by reaction-diffusion equations. Viable cells consume the nutrients, which are converted into biomass by increasing the cell size during the G1 phase. We test hypotheses on the functional dependence of the uptake rates and use computer simulations to find suitable mechanisms for the induction of necrosis. This is done by comparing the outcome with experimental growth curves, where the best fit leads to an unexpected ratio of oxygen and glucose uptake rates. The model relies on physical quantities and can easily be generalized towards tissues involving different cell types. In addition, it provides many features that can be directly compared with the experiment.

Pattern of self-organization in tumour systems: complex growth dynamics in a novel brain tumour spheroid model

We propose that a highly malignant brain tumour is an opportunistic, self-organizing and adaptive complex dynamic biosystem rather than an unorganized cell mass. To test the hypothesis of related key behaviour such as cell proliferation and invasion, we have developed a new in vitro assay capable of displaying several of the dynamic features of this multiparameter system in the same experimental setting. This assay investigates the development of multicellular U87MGmEGFR spheroids in a specific extracellular matrix gel over time. The results show that key features such as volumetric growth and cell invasion can be analysed in the same setting over 144 h without continuously supplementing additional nutrition. Moreover, tumour proliferation and invasion are closely correlated and both key features establish a distinct ratio over time to achieve maximum cell velocity and to maintain the system's temporo-spatial expansion dynamics. Single cell invasion follows a chain-like pattern leading to the new concept of a intrabranch homotype attraction. Since preliminary studies demonstrate that heterotype attraction can specifically direct and accelerate the emerging invasive network, we further introduce the concept of least resistance, most permission and highest attraction as an essential principle for tumour invasion. Together, these results support the hypothesis of a self-organizing adaptive biosystem.

Simulated brain tumor growth dynamics using a three-dimensional cellular automaton

We have developed a novel and versatile three-dimensional cellular automaton model of brain tumor growth. We show that macroscopic tumor behavior can be realistically modeled using microscopic parameters. Using only four parameters, this model simulates Gompertzian growth for a tumor growing over nearly three orders of magnitude in radius. It also predicts the composition and dynamics of the tumor at selected time points in agreement with medical literature. We also demonstrate the flexibility of the model by showing the emergence, and eventual dominance, of a second tumor clone with a different genotype. The model incorporates several important and novel features, both in the rules governing the model and in the underlying structure of the model. Among these are a new definition of how to model proliferative and non-proliferative cells, an isotropic lattice, and an adaptive grid lattice.

Cellular automaton of idealized brain tumor growth dynamics

A novel cellular automaton model of proliferative brain tumor growth has been developed. This model is able to simulate Gompertzian tumor growth over nearly three orders of magnitude in radius using only four microscopic parameters. The predicted composition and growth rates are in agreement with a test case pooled from the available medical literature. The model incorporates several new features, improving previous models, and also allows ready extension to study other important properties of tumor growth, such as clonal competition.

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.

Three-dimensional culture of human tumor cells under standardized medium conditions

The 3-dimensional culture of human tumor spheroids under standardized medium conditions may reveal information on specific biological parameters that could be masked in serum-supplemented media. Spheroids derived from human tumor cells are growth retarded in media free of serum. Ex-Cyte IV is a substance derived from human blood that can be used to improve growth in tissue culture. In this study the growth of spheroids from four different human tumor cell lines was studied when grown in medium free of serum, medium supplemented with varying concentrations Ex-Cyte IV, and medium supplemented with foetal calf serum (FCS). The parameters used for comparisons were growth rate, growth enhancement, clonogenicity and cell cycle distribution. The four cell lines showed different growth rates in serum-free medium, which were increased to different extents when Ex-Cyte IV or FCS were added. The growth enhancing effect induced by Ex-Cyte IV was differently concentration dependent for each cell line. The clonogenicity of cells grown as spheroids in serum-free medium was lower than in spheroids grown in supplemented media. There was no difference in clonogenicity between the differently supplemented media. All four cell lines responded to growth in serum-free medium with a drop in the S-phase and G2M phase. The present study provides a novel approach to the study of human tumor cells in 3-dimensional culture under defined conditions. The human serum derived substance Ex-Cyte IV may provide a method to obtain information on specific biological parameters that could be masked in serum-supplemented media.

Multicell spheroids as a model for cell kinetic studies

Cells growing in tissue culture as three-dimensional, multicellular aggregates called 'spheroids' typically show a decreasing growth fraction and development of quiescent subpopulations as the spheroids enlarge. Kinetic studies in a number of spheroid systems have indicated that the primary reason for the tumour-like growth is a progressive decrease in growth fraction, with only a modest elongation of cell cycle time in larger spheroids. In this paper, the cellular growth kinetics for spheroids of V79 Chinese hamster lung cells are reviewed, and the regrowth kinetics of cells resuming growth after recovery from quiescent regions of the spheroids are described. Further, the role of regrowth/repopulation in determining the spheroid response to anti-tumour cytotoxics is explored, with particular emphasis on treatment with cisplatin and etoposide. By separating the effects of cytotoxicity and regrowth in the overall spheroid response to anti-neoplastic drugs, it is suggested that 'drug resistance' in tumours can be a kinetic as well as a genetic problem.

Continuous stressing of mouse interparietal suture fibroblasts in vitro

The morphological and biochemical response of sutural fibroblasts in vitro to continuous force was examined. Cells from mouse interparietal sutures were grown and subcultured on glass slides. Titanium disks coated with collagen were allowed to attach to the cellular multilayers. Four of the glass slides were then placed at an angle of 75 degrees for a period of three days so that continuous stress would be created, while four others were left flat. Also, four glass slides were left flat with no disk. Following the incubation period, the dishes were labeled with 14C-glycine for 15 h. The cells and medium were then collected for collagen extraction followed by SDS-polyacrylamide gel electrophoresis. Dried gels impregnated with fluor were exposed to x-ray films that were then scanned densitometrically for collagen types I and III. It was found that the proportion of newly-synthesized type III collagen increased significantly with the application of continuous stress. A second set of experimental and control glass slides was fixed in glutaraldehyde and post-fixed in osmium tetroxide. Following critical-point drying and coating, the glass slides were examined under a scanning electron microscope. The scanning images showed the formation of a ligament-like structure between the disk and the glass slide. Moreover, mitotic activity, as evidenced by spheroidal cells, was stimulated in the areas previously adjacent to the disc, which had since moved away. This system offers a standardized continuous force system that can stress cells in a ligament-like structure and thus provides an in vitro model analogous to clinical orthodontic and orthopedic stress.

Swelling of multicellular spheroids induced by hyperthermia

EMT6 multicellular spheroids invariably swell by 10 to 50 per cent after incubation at 43 to 45 degrees C for 1 h. Both scanning electron and optical microscopy reveal morphological alterations particularly in the outer region of the spheroids. While the control cells are contiguous to one another and tightly held to the spheroid body, the heated spheroids exhibit partially disrupted contacts among cells. Measurements of intercellular volume and water volume of spheroids with labelled water and inulin show that changes in the spheroid volume are not due to an increase in cell volume, but that they can be explained by a 60-100 per cent increase in the intercellular space within a spheroid. Continuous observation of individual spheroids heated to 43-45 degrees C shows loss of adhesion of cells in the outer region and even detachment of a few surface cells. This 'melting' of the spheroid surface appears to result from a disorder in the extracellular material. Treatment with cell swelling agents such as hypotonic solution, ouabain, excess extracellular potassium ions, or ionophore nigericin, K+/H+ exchanger, each separately causes the spheroids to swell at the control temperature. On the other hand, A23187, Ca2+ ionophore, causes shrinkage of the spheroids. Thus, under hyperthermia, the volume of spheroids increases due to the disruption in the cell organization in their outer region.

Multicellular spheroids. A review on cellular aggregates in cancer research

Cellular aggregates have been used in developmental biology and in experimental cancer research for several decades. Spherical aggregates of malignant cells, i.e. multicellular tumor spheroids, may serve as in vitro models of tumor microregions and of an early, avascular stage of tumor growth. The similarities between the original tumor and the respective spheroids include volume growth kinetics, cellular heterogeneity, e.g. the induction of proliferation gradients and quiescence, as well as differentiation characteristics, such as the development of specific histological structures or the expression of antigens. Research using cell aggregates has been focussed on mechanisms involved in the control of proliferation, invasion and metastasis. Immunological studies with spheroids have resulted in the characterization of defense cells which are responsible for specific host-versus-tumor reactions. The vast majority of investigations on spheroids concerns the simulation of therapy with regard to various treatment modalities, combination treatments and systematic analyses of using various endpoints in predictive assays. Only a few pathophysiological studies on the interrelationship among tumor-specific micromilieu, cellular metabolism, proliferative status, and cellular viability have been undertaken with the spheroid model up to now. Since these studies are indicative of a large influence of the cellular microenvironment on basic biological properties of cancer cells, investigations of these epigenetic mechanisms should be intensified in future research on cell aggregates. Similarly, the molecular basis of the biological peculiarities found in malignant cells grown as three-dimensional aggregates has to be investigated more intensively.

Spontaneous cell shedding by tumor cells in monolayer culture

Sarcoma 180 monolayers spontaneously shed single cells and small multicellular aggregates into the surrounding medium to produce a dual population of floating and substratum-attached cells. Shedding was a motility-associated event that occurred when cells attempted to migrate over one another. It resulted from a combination of cell shape change and active motility, which increased sensitivity to fluid shear dislodgement by reducing a cell's surface area of adhesive contact and increasing strain tension at its adhesive contact points. Shedding occurred at all phases of the cell cycle. Extracellular matrix but not conditioned medium enhanced the floating subpopulation by slowing the kinetics of reattachment to plastic and cellular substrate. Although sarcoma 180 cells are anchorage independent in the sense that they grow readily in single cell suspension, they nevertheless exhibited anchorage modulation of their cell cycle. Short periods in suspension produced a mild G1 accumulation, whereas longer periods of anchorage deprivation led to a mild G2 accumulation which appeared to result from an interference with cytokinesis.

Dynamics of cell kinetic parameters during 9L spheroid growth

Cell population kinetics were followed in 9L tumour spheroids as they grew from aggregates of about 80 micron in diameter to over 800 micron. The kinetic parameters measured were cell cycle time, spheroid-doubling time, and growth fraction; from these the cell loss factor phi was calculated. The rate of cell shedding from the surface was also measured, so that the contribution of shedding to the overall cell loss could be evaluated. The major findings include significant elongation of the cell cycle, a low rate of cell death in spheroids below 500 micron in diameter, and a relatively high GF in large spheroids. The results also indicated that 9L spheroid kinetic parameters may be strongly influenced by the culture methodology.

Growth and characterization of multicellular tumor spheroids of human bladder carcinoma origin

We have examined the MGH-U1 human bladder carcinoma cell line and 12 primary bladder carcinoma biopsies for their ability to form spheroids in suspension culture and in multiwell dishes. MGH-U1 cells formed tightly packed spheroids with a necrotic center and viable rim whereas three sublines formed loose aggregates only. Spheroids formed from as few as 100 MGH-U1 cells placed into multiwells. MGH-U1 cells derived from spheroids formed new spheroids more rapidly and and consistently than cells derived from monolayer culture. Spheroid diameter increased at a rapid rate of approximately 100 microns/d in multiwell dishes, and necrosis occurred only in spheroids of diameter greater than 1 mm. Spheroids placed in spinner culture at a higher concentration (approximately 1.5 spheroids/ml) grew more slowly and developed necrosis at smaller diameters. The width of the viable rim of spheroids grown in spinner culture was maintained at approximately 190 microns over a wide range of spheroid diameters (400 to 1000 microns). Sequential trypsinization of spheroids, which stripped layers of cells from the spheroids, demonstrated no difference in the plating efficiency of cells derived from varying depths into the spheroid. Only one of the 12 primary bladder biopsy specimens demonstrated an ability to form spheroids. This biopsy, designated HB-10, formed spheroids that grew linearly over 40 d, formed colonies in methylcellulose culture and grew as xenografts in immune-deprived mice. These studies characterize the MGH-U1 spheroids that are useful in vitro models to study the effects of various treatments for solid tumors and demonstrate the limited capacity of cells from primary human bladder biopsies to form spheroids.

Growth and cellular characteristics of multicell spheroids

The data reviewed here demonstrate that there are many similarities in growth and cellular characteristics for different types of tumor cells grown as multicell spheroids. Furthermore, where comparisons have been made many of the features of spheroids also occur in tumors in vivo. However, as for tumors, there are also many characteristics of individual types of spheroids which are relatively specific and cannot be generalized as properties of all spheroid model systems. The results also demonstrate the marked influence which cellular microenvironments regulated by a supply of oxygen and nutrients may have on the development of cellular heterogeneity. Furthermore, using spheroids it was shown that dynamic cellular and metabolic interactions exist in regulating the development of cellular subpopulations and microenvironments. Spheroids are more sensitive to alterations in culture environment than are monolayer or single-cell suspension cultures. Consequently, researchers who use this model system must characterize, optimize, and standardize the growth conditions for the spheroid cell type being investigated. This information then provides a base from which to undertake detailed studies, which are not possible in experimental tumors, of controlled manipulation of microenvironments in spheroids. The ranges of cellular microenvironments and cellular heterogeneity which exist at different stages of spheroid growth provide a model, at least in part, for coexisting size ranges of microregions in many solid tumors. Thus, spheroids provide a model, which at different stages of growth is readily manipulated and controlled experimentally, to facilitate studies of contributions of individual environmental factors, or concomitant changes in these, on cellular phenotypic expression. It is probable that the cellular changes which can be demonstrated to occur during spheroid growth, also occur in vivo. Modulation of cellular characteristics revealed by research with spheroids requires much more study to determine the mechanisms and effects on tumor cell behavior, as well as response to therapeutic agents and their relevance to tumors in vivo.

A model for the growth of multicellular spheroids

Based on biological observations and the basic physical properties of tri-dimensional structures, a mathematical expression is derived to relate the growth rate of multicellular spheroids to some easily measurable parameters. This model involves properties both of the individual cells and of the spheroid structure, such as the cell doubling time in monolayer, the rate of cell shedding from the spheroid and the depth of the external rim of cycling cells. The derived growth equation predicts a linear expansion of the spheroid diameter with time. The calculated growth rate for a number of spheroid cell types is in good agreement with experimental data. The model provides a simple and practical view of growth control in spheroids, and is further adapted to include parameters presumably responsible for the growth saturation in large spheroids.

Development of tetraploidy in V79 spheroids

Chinese hamster V-79-171 cells, when placed in suspension culture, spontaneously form multicell spheroids. As the spheroids enlarge the fraction of polyploid (predominantly tetraploid) cells increases and can approach 100% in very large spheroids. Spheroid size, rather than age, seems to be a major determinant for increased ploidy. When cell separation techniques were used to select enriched populations of diploid and tetraploid cells, the growth rate and plating efficiency of the diploid cells was always marginally higher, and they gradually became predominant in mixed monolayer cultures. Cloned tetraploid cells, however, generally remained quite stable, and no consistent ploidy dependent changes in radiosensitivity were observed relative to normal, diploid cell lines.

Growth and functional activities of neonatal and adult rat hepatocytes cultured on fibronectin coated substratum in serum-free medium

Hepatocytes isolated from neonatal (NN) and adult (AD) rats were seeded on fibronectin coated substratum and cultured in arginine-free medium supplemented with various combinations of insulin, dexamethasone, triiodothyronine (T3), albumin, and transferrin, in presence or absence of fibronectin depleted serum (FDS). The main finding is that in response to certain hormone mixtures, both NN and AD hepatocytes can be stimulated to proliferate, as revealed by an increase in cell number, a [3H]thymidine incorporation into nuclei, and extractable DNA as well as the appearance of mitotic figures. Moreover, this proliferative activity is associated with changes in hepatocyte ploidy. However, the proliferative response of NN hepatocytes to hormone action is much different from that of AD hepatocytes, and the addition of FDS amplifies this activity in NN but inhibits it in AD hepatocyte cultures. Measurements of tyrosine aminotransferase and lactate dehydrogenase activities indicate a good preservation of NN and AD hepatocyte functional integrity under certain culture conditions. A good maintenance of albumin production in NN and AD hepatocyte cultures requires the presence of dexamethasone, whereas the alpha-fetoprotein production in NN hepatocyte cultures is reduced quite rapidly under most conditions. No alpha-fetoprotein is detectable in AD hepatocyte cultures.