Invited review Multicell spheroids as a model for cell kinetic studies

Abstract. 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.     

Regrowth kinetics of cells from different regions of multicellular spheroids of four cell lines

A basic understanding of the recruitment of quiescent tumor cells into the cell cycle would be an important contribution to tumor biology and therapy. As a first step in pursuing this goal, we have investigated the regrowth kinetics of cells from different regions in multicellular spheroids of rodent and human origin. Cells were isolated from four different depths within the spheroids using a selective dissociation technique. The outer cells were proliferating and resumed growth after replating with a 0-8-hour lag period, similar to cells from exponentially growing monolayers. With increasing depth of origin, the lag periods prior to regrowth increased to 2-3 times the monolayer doubling time; cells from plateau-phase monolayers showed a lag period of 1-1.5 times the doubling period. After resuming growth, all cells of a given cell line grew with the same doubling time and achieved the same confluency level. The inner spheroid cells and cells from plateau-phase monolayers had reduced clonogenic efficiencies. The inner cells were initially 1.5-3 times smaller than the outer cells, but began to increase in volume within 4 hours of replating. The fractions of S-phase cells were greatly decreased with increasing depth of origin in the spheroids; there were long delays prior to S-phase recovery after plating, to a maximum of 1-1.5 times the normal doubling time. These results suggest that those quiescent cells from spheroids and monolayers which are able to reenter the cell cycle are predominantly in the G1-phase. However, quiescent cells from the innermost spheroid region require approximately twice as long to enter normal cell cycle traverse as cells from plateau-phase monolayers. The selective dissociation method can isolate very pure populations of proliferating and quiescent cells in a rapid and nonperturbing manner; this system will be valuable in further characterizing quiescent cells from spheroids.     

Visualizing the effect of tumor microenvironments on radiation-induced cell kinetics in multicellular spheroids consisting of HeLa cells

In this study, we visualized the effect of tumor microenvironments on radiation-induced tumor cell kinetics. For this purpose, we utilized a multicellular spheroid model, with a diameter of ∼500 μm, consisting of HeLa cells expressing the fluorescent ubiquitination-based cell-cycle indicator (Fucci). In live spheroids, a confocal laser scanning microscope allowed us to clearly monitor cell kinetics at depths of up to 60 μm. Surprisingly, a remarkable prolongation of G2 arrest was observed in the outer region of the spheroid relative to monolayer-cultured cells. Scale, an aqueous reagent that renders tissues optically transparent, allowed visualization deeper inside spheroids. About 16 h after irradiation, a red fluorescent cell fraction, presumably a quiescent G0 cell fraction, became distinct from the outer fraction consisting of proliferating cells, most of which exhibited green fluorescence indicative of G2 arrest. Thereafter, the red cell fraction began to emit green fluorescence and remained in prolonged G2 arrest. Thus, for the first time, we visualized the prolongation of radiation-induced G2 arrest in spheroids and the differences in cell kinetics between the outer and inner fractions.     

A reduction in the in situ rates of oxygen and glucose consumption of cells in EMT6/Ro spheroids during growth

The rates of consumption of oxygen and glucose by EMT6/Ro cells in multicellular spheroids were measured at various times during normal growth. In situ spheroid cellular consumption rates were similar to those of exponentially growing single cells up to a spheroid diameter of 150 micron. Further growth resulted in decreases in the rates of both oxygen and glucose consumption which were correlated with the increase in spheroid diameter and cell number. At a diameter of 1300 micron, both rates of cellular consumption had decreased by a factor of 2.5. The rates of consumption per unit of nonnecrotic spheroid volume decreased in a similar manner. Measurements with single cells demonstrated that the rate of oxygen consumption was coupled with glucose concentration, and vice versa. The rates of consumption for cells dissociated from small spheroids indicated that there was some effect of the spheroid environment. As the spheroids grew, however, association in the spheroid structure accounted for a smaller proportion of the total observed reduction in the rates of nutrient consumption. The presence of central necrosis also appeared to have no effect on the rates of consumption of these nutrients. Spheroid-derived cells showed a decrease in cell volume with growth as the cells accumulated in a quiescent state. Measurements with single cells demonstrated that oxygen and glucose consumption were correlated with cell volume and with the development of nonproliferating cells. We conclude that the observed decrease in oxygen and glucose consumption with growth in spheroids is largely due to the progressive accumulation of cells in a quiescent state characterized by an inherently lower cellular rate of nutrient utilization.     

In situ oxygen consumption rates of cells in V-79 multicellular spheroids during growth

The rate of consumption of oxygen by V-79 cells in multicellular spheroids was measured as a function of the spheroid diameter. In situ consumption was equal to that of exponentially growing cells for spheroids less than 200 micron in diameter. The rate of oxygen consumption decreased for cells in spheroids between 200 and 400 micron diameter to a value one-fourth the initial, then remained constant with further spheroid growth. Comparison of consumption rates for spheroid-derived cells before and after dissociation from the spheroid structure indicated that the spheroid microenvironment accounted for only 20% of the change in oxygen consumption rate. Cell-cell contact, cell packing, and cell volume were not critical parameters. Plateau-phase cells had a fivefold lower rate of oxygen consumption than exponential cells, and it is postulated that the spheroid quiescent cell population accounts for a large part of the intrinsic alteration in oxygen consumption of cells in spheroids. Some other mechanism must be involved in the regulation of cellular oxygen consumption in V-79 spheroids to account for the remainder of the reduction observed in this system.     

Automated selective dissociation of cells from different regions of multicellular spheroids

Summary In this report we describe a new apparatus which has been developed for the automated selective dissociation of multicellular spheroids into fractions of viable cells from different locations in the spheroid. This device is based on the exposure of spheroids to a 0.25% solution of trypsin under carefully controlled conditions, such that the cells are released from the outer spheroid surface in successive layers. Study of the spheroid size, number of cells per spheroid, and sections through the spheroid with increasing exposure to trypsin demonstrate the effectiveness of this technique. The technique has been successfully used on spheroids from five different cell lines over a wide range of spheroid diameters. We also present data detailing the effect of varying the dissociation temperature, the mixing speed, the trypsin concentration, and the number of spheroids being dissociated. The new apparatus has several advantages over previous selective dissociation methods and other techniques for isolating cells from different regions in spheroids, including: a) precise control over dissociation conditions, improving reproducibility; b) short time to recover cell fractions; c) ability to isolate large numbers of cells from many different spheroid locations; d) use of common, inexpensive laboratory equipment; and e) easy adaptability to new cell lines or various spheroid sizes. Applications of this method are demonstrated, including the measurement of nutrient consumption rates, regrowth kinetics, and radiation survivals of cells from different spheroid regions. This work was supported by grants CA-36535, CA-22585, and RR-02845 from the National Institutes of Health, Bethesda, MD, the National Flow Cytometry Resource (NIH grant RR-01315), and by the Department of Energy, Washington, DC.     

Modeling of self-organized avascular tumor growth with a hybrid cellular automaton

Pattern formation in multicellular spheroids is addressed with a hybrid lattice-gas cellular automaton model. Multicellular spheroids serve as experimental model system for the study of avascular tumor growth. Typically, multicellular spheroids consist of a necrotic core surrounded by rings of quiescent and proliferating tumor cells, respectively. Furthermore, after an initial exponential growth phase further spheroid growth is significantly slowed down even if further nutrient is supplied. The cellular automaton model explicitly takes into account mitosis, apoptosis and necrosis as well as nutrient consumption and a diffusible signal that is emitted by cells becoming necrotic. All cells follow identical interaction rules. The necrotic signal induces a chemotactic migration of tumor cells towards maximal signal concentrations. Starting from a small number of tumor cells automaton simulations exhibit the self-organized formation of a layered structure consisting of a necrotic core, a ring of quiescent tumor cells and a thin outer ring of proliferating tumor cells.     

Recovery from potentially lethal damage and recruitment time of noncycling clonogenic cells in 9L confluent monolayers and spheroids

Cells that have been grown as multicell tumor spheroids exhibit radioresistance compared to the same cells grown in monolayers. Comparison of potentially lethal damage (PLD) repair and its kinetics was made between 9L cells grown as spheroids and confluent monolayers. Survival curves of cells plated immediately after irradiation showed the typical radioresistance associated with spheroid culture compared to plateau-phase monolayers. The dose-modification factor for spheroid cell survival is 1.44. Postirradiation incubations in normal phosphate-buffered saline (PBS), conditioned media, or 0.5 M NaCl in PBS reduced the differences in radiosensitivity between the two culture conditions. Postirradiation treatment in PBS or conditioned medium promoted repair of potentially lethal damage, and 0.5 M NaCl prevented the removal of PLD and allowed the fixation of damage resulting in lower survival. Survival of spheroid and monolayer cells after hypertonic NaCl treatment was identical. NaCl treatment reduced Do more than it did the shoulder (Dq) of the survival curve. PLD repair kinetics measured after postirradiation incubation in PBS followed by hypertonic NaCl treatment was the same for spheroids and for plateau-phase monolayers. The kinetics of PLD repair indicates a biphasic phenomenon. There is an initial fast component with a repair half-time of 7.9 min and a slow component with a repair half-time of 56.6 min. Most of the damage (59%) is repaired slowly. Since the repair capacity and kinetics are the same for spheroids and monolayers, the radioresistance of spheroids cannot be explained on this basis. Evidence indicates that the time to return from a Go (noncycling G1 cells) state to a proliferative state (recruitment) for cells from confluent monolayers and from spheroids after dissociation by protease treatment may be the most important determinant of the degree of PLD repair that occurs. Growth curves and flow cytometry cell cycle analysis indicate that spheroid cells have a lag period for reentry into a proliferative state. Since plating efficiency remains high and unchanging during this period, one cannot account for the delay on the basis of the existence of a large fraction of Go cells which are not potentially clonogenic. The cell cycle progression begins in 6-8 h for monolayer cells and in 14-15 h for spheroids. It is hypothesized that the slower reentry of spheroid cells into a cycling phase allows more time for repair than for the rapidly proliferating monolayer cells.     

Formation of multicellular spheroids composed of adult rat hepatocytes in dishes with positively charged surfaces and under other nonadherent environments

Adult rat hepatocytes formed floating multicellular spheroids in primary culture in an uncoated plastic dish with a positively charged surface. Cells in the spheroids formed in such a simple way were similar to those formed in dishes coated with proteoglycan fraction isolated from rat liver reticulin fibers; in both cases, cells maintained high ability to produce albumin and poor ability to proliferate in response to epidermal growth factor. Coating dishes with albumin was also helpful in spheroid formation; coating with 2-hydroxymethyl methacrylate resulted in formation of incomplete spheroids. Elimination of serum factors was essential for the formation of spheroids; when cells were washed with serum-containing medium before seeding or if the medium was replaced with a serum-containing medium, spheroid formation was completely inhibited. Collagens, fibronectin, and laminin, all of which promote the adhesion and spreading of hepatocytes on substrates, inhibited spheroid formation. Furthermore, collagens disintegrated spheroids, and cells in the monolayer initiated proliferation. Thus, two distinct, mutually exclusive features of primary culture of adult hepatocytes apparently exist; monolayer culture with proliferative activity in an adherent environment and spheroid culture with poor proliferative activity and high albumin-producing ability in a nonadherent environment.     

β1 Integrins restrict the growth of foci and spheroids

Extracellular matrices (ECM) have important roles for tissue architecture, both as structural and signaling components. Members of the integrin family are the main regulators of ECM assembly and transmitters of signals from the ECM to cells. In this study, we have analyzed the role of integrin subunit β1 in two-dimensional (2D) and three-dimensional (3D) cell cultures using integrin β1 null cells (MEFβ1^?/? and GD25) and their β1 integrin-expressing counterparts. GD25 and GD25β1 cells proliferated with similar kinetics in sub-confluent 2D cultures, whereas GD25 cells attained higher cell numbers in confluent culture and formed foci with fivefold higher frequency than GD25β1 cells. Fibronectin fibrils were abundantly deposited throughout the GD25β1 colonies but strictly limited to the central multilayered area (focus) of GD25 colonies. During 3D growth as spheroids, GD25 continuously increased in size for >21?days while the growth of GD25β1 spheroids ceased after 14?days. Similarly, MEFβ1^?/? cells formed foci and grew as spheroids, while the β1 integrin-expressing MEF did not. Expression levels of the cell cycle markers Ki67, PCNA, and histone H3-pSer10 were similar between GD25β1 and GD25 spheroids. Apoptotic cells accumulated earlier in GD25 spheroids; however, cell death increased with spheroid volumes in both spheroid types. In both cell systems, the presence of β1 integrins resulted in higher levels of active myosin light chain and inactive myosin light chain phosphatase, and a more compact spheroid structure. In conclusion, our results reveal that regulation of 3D growth in spheroids and foci is dependent on the β1 subfamily of integrins, and suggest that myosin-based spheroid contraction in combination with cell death limits the growth of β1-expressing spheroids.     

The effect of combined heat and ultrasound on multicellular tumour spheroids

The effect of combined ultrasound and heat treatments on Chinese hamster multicellular spheroids of varying size was investigated using growth rate, single cell survival and ultrastructural damage as endpoints. Ultrasonic irradiation at 37 degrees C had no effect on the growth rate of 200-730 microns spheroids. Similarly there was no effect on the growth rate of 350 microns spheroids when irradiated during a 60 min exposure to 41.5 degrees C. However, spheroids of 200-700 mm diameter showed growth delay when held at 43 degrees C for 1 h. The effect was enhanced with concomitant ultrasound irradiation but was not dependent on spheroid size. When 200 and 400 microns spheroids held at 43 degrees C for 60 min were irradiated with different ultrasonic intensities a dose-dependent decrease in surviving fraction and a dose-dependent increase in growth delay was obtained. When surviving fraction was plotted as a function of growth delay a good correlation was obtained, suggesting that the combination of heat and ultrasound irradiation does not produce cytostasis in the surviving cells of either 200 or 400 microns spheroids. At the ultrastructural level increased cytoplasmic vacuolation was the only result of ultrasonic irradiation at 37 degrees C. Exposure to 43 degrees C for 60 min was required to elicit thermal damage. This took the form of membrane evagination at the spheroid surface, vacuolation of the cytoplasm, grouping of organelles around the periphery of the nucleus, and fragmentation of the nucleolus. These effects were enhanced with concomitant ultrasonic irradiation but other features were also noted, viz. disaggregation of polyribosomes, dilation of the rough endoplasmic reticulum and blebbing of the nuclear membrane. Damage was independent of spheroid size. These results are in agreement with previous data obtained from single-cell studies. Indicating that there is a non-thermal, non-cavitational component to the cell killing in multicellular spheroids resulting from combined heat and ultrasound treatment.     

Decreased mitochondrial function in quiescent cells isolated from multicellular tumor spheroids

Cells in the inner region of multicellular spheroids markedly reduce their oxygen consumption rate, presumably in response to their stressful microenvironment. To determine the mechanism behind this metabolic adaptation, we have investigated relative mitochondrial mass and mitochondrial function in cells isolated from different regions of tumor spheroids by using a combination of mitochondrial-specific fluorescent stains and flow cytometric analysis. Uptake of rhodamine 123 (R123) is driven by the mitochondrial membrane potential and thus reflects mitochondrial activity. Uptake of 10-nonyl-acridine orange (NAO) reflects total mitochondrial mass independently of activity because this compound binds to cardiolipin in the inner mitochondrial membrane. NAO fluorescence per unit cell volume only decreased 10–20% for cells from the inner spheroid region compared with those near the surface. There was greater than a twofold reduction in R123 fluorescence in the inner region cells, however. Thus, tumor cells in spheroids alter their rate of respiration predominately by downregulating mitochondrial function as opposed to degradation of mitochondria. There was a correlation between R123 staining per unit cell volume and the growth fraction of the cells from spheroids, but not for monolayer cultures. We also show a linear correlation between R123 staining and the rate of oxygen consumption for both monolayer- and spheroid-derived cells. After separating the inner region cells from the spheroid and replating them in monolayer culture, the R123 uptake recovered to normal levels prior to entry of the cells into S-phase. This reduction in mitochondrial function in quiescent cells from spheroids can explain the long period required for these cells to re-enter the cell cycle and may have important implications for the regulation of tumor cell oxygenation in vivo. J. Cell. Physiol. 176:138–149, 1998. Published 1998 Wiley-Liss, Inc.

1 This article is a US Government work and, as such, is in the public domain in the United States of America.

     

Dynamics of spheroid self-assembly in liquid-overlay culture of DU 145 human prostate cancer cells.

The in vitro self-assembly of multicellular spheroids generates highly organized structures in which the three-dimensional structure and differentiated function frequently mimic that of in vivo tissues. This has led to their use in such diverse applications as tissue regeneration and drug therapy. Using Smoluchowski-like rate equations, herein we present a model of the self-aggregation of DU 145 human prostate carcinoma cells in liquid-overlay culture to elucidate some of the physical parameters affecting homotypic aggregation in attachment-dependent cells. Experimental results indicate that self-aggregation in our system is divided into three distinct phases: a transient reorganization of initial cell clusters, an active aggregation characterized by constant rate coefficients, and a ripening phase of established spheroid growth. In contrast to the diffusion-controlled aggregation previously observed for attachment-independent cells, the model suggests that active aggregation in our system is reaction-controlled. The rate equations accurately predict the aggregation kinetics of spheroids containing up to 30 cells and are dominated by spheroid adhesive potential with lesser contributions from the radius of influence. The adhesion probability increases with spheroid size so that spheroid-spheroid adhesions are a minimum of 2.5 times more likely than those of cell-cell, possibly due to the upregulation of extracellular matrix proteins and cell-adhesion molecules. The radius of influence is at least 1.5 to 3 times greater than expected for spherical geometry as a result of ellipsoidal shape and possible chemotactic or Fr?hlich interactions. Brownian-type behavior was noted for spheroids larger than 30 microm in diameter, but smaller aggregates were more motile by as much as a factor of 10 for single cells. The model may improve spheroid fidelity for existing applications of spheroids and form the basis of a simple assay for quantitatively evaluating cellular metastatic potential as well as therapies that seek to alter this potential.     

A model for the growth of multicellular spheroids

Abstract. 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.     

Mathematical modelling of drug transport in tumour multicell spheroids and monolayer cultures

In this paper we adapt an avascular tumour growth model to compare the effects of drug application on multicell spheroids and on monolayer cultures. The model for the tumour is based on nutrient driven growth of a continuum of live cells, whose birth and death generates volume changes described by a velocity field. The drug is modelled as an externally applied, diffusible material capable of killing cells, both linear and Michaelis-Menten kinetics for drug action on cells being studied. Numerical solutions of the resulting system of partial differential equations for the multicell spheroid case are compared with closed form solutions of the monolayer case, particularly with respect to the effects on the cell kill of the drug dosage and of the duration of its application. The results show an enhanced survival rate in multicell spheroids compared to monolayer cultures, consistent with experimental observations, and indicate that the key factor determining this is drug penetration. An analysis of the large time tumour spheroid response to a continuously applied drug at fixed concentration reveals up to three stable large time solutions, namely the trivial solution (i.e. a dead tumour), a travelling wave (continuously growing tumour) and a sublinear growth case in which cells reach a pseudo-steady-state in the core. Each of these possibilities is formulated and studied, with the bifurcations between them being discussed. Numerical solutions reveal that the pseudo-steady-state solutions persist to a significantly higher drug dose than travelling wave solutions.     

Recovery of thioguanine-resistant cells from Chinese hamster V79 spheroids

Multicell spheroids may prove useful in evaluting the interactions of mutagens with cells exposed in a tissue-like environment. However, direct comparisons among populations of Chinese hamster V79 spheroids of different sizes or with monolayers are complicated by the observation that as spheroids enlarge, the fraction of mutant cells resistant to 6-thioguanine (TG^r) gradually decreases from about 5 in 10⁵ to less than 1 in 10⁵. There appear to be at least 2 explanations for these observations. First, TG^r cells grow less well as spheroids than do 6-thioguanine-sensitive (TG^s) cells. Second, the clonal nature of spheroid growth means that small samples fo spheroids are likely to contain fewer pre-existing TG^r cells.     

The migration of cells in multicell tumor spheroids

A mathematical model is proposed to explain the observed internalization of microspheres and 3H-thymidine labelled cells in steady-state multicellular spheroids. The model uses the conventional ideas of nutrient diffusion and consumption by the cells. In addition, a very simple model of the progress of the cells through the cell cycle is considered. Cells are divided into two classes, those proliferating (being in G1, S, G2 or M phases) and those that are quiescent (being in G0). Furthermore, the two categories are presumed to have different chemotactic responses to the nutrient gradient. The model accounts for the spatial and temporal variations in the cell categories together with mitosis, conversion between categories and cell death. Numerical solutions demonstrate that the model predicts the behavior similar to existing models but has some novel effects. It allows for spheroids to approach a steady-state size in a non-monotonic manner, it predicts self-sorting of the cell classes to produce a thin layer of rapidly proliferating cells near the outer surface and significant numbers of cells within the spheroid stalled in a proliferating state. The model predicts that overall tumor growth is not only determined by proliferation rates but also by the ability of cells to convert readily between the classes. Moreover, the steady-state structure of the spheroid indicates that if the outer layers are removed then the tumor grows quickly by recruiting cells stalled in a proliferating state. Questions are raised about the chemotactic response of cells in differing phases and to the dependency of cell cycle rates to nutrient levels.     

CELL CYCLE KINETICS IN AN IN VITRO TUMOR MODEL

Cell cycle kinetic parameters of multicell spheroids in vitro have been estimated using thymidine labeling techniques and autoradiography. Both the mitotic index and thymidine labeling index decreased in larger spheroids, whereas the duration of the cell cycle, as determined by two independent methods utilizing labeled mitoses or labeled cells, was essentially independent of spheroid size or age. These results suggest that the tumor-like growth exhibited by spheroids is the result of a decreasing growth fraction and a large apparent cell loss, rather than a general elongation of the cell cycle.     

Parameter estimation and determinability analysis applied to Drosophila gap gene circuits

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.